Fun\303\247\303\243o do Segundo Grau:A F\303\263rmula Quadr\303\241tica<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Motiva\303\247\303\243o</Font></Text-field>A solu\303\247\303\243o da equa\303\247\303\243o quadr\303\241tica 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 \303\251 dada pela f\303\263rmula quadr\303\241tica, ou seja, pela 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 \303\251 obtido completando o quadrado no lado esquerdo da equa\303\247\303\243o quadr\303\241tica. Esta f\303\263rmula pode ser aplicada em qualquer equa\303\247\303\243o quadr\303\241tica, mesmo aquelas que n\303\243o cedem \303\240 t\303\251cnica de factora\303\247\303\243o. \303\211 interessante que historicamente, ap\303\263s a descoberta da f\303\263rmula quadr\303\241tica, os matem\303\241ticos procuraram f\303\263rmulas para resolver equa\303\247\303\265es polinomiais de grau mais elevado. H\303\241 receitas para resolver equa\303\247\303\265es polinomiais de grau tr\303\252s e quatro, mas foi provado que n\303\243o existe nenhuma f\303\263rmula para equa\303\247\303\265es de grau cinco ou superior. N\303\243o \303\251 que ningu\303\251m encontrou ainda a f\303\263rmula\342\210\222a prova demonstra que n\303\243o existe nenhuma f\303\263rmula.Cr\303\251dito para isso \303\251 dada a um jovem franc\303\252s chamado Everiste Galois (1811 - 1832) que, quando ainda era adolescente, determinou as condi\303\247\303\265es necess\303\241rias e suficientes para uma equa\303\247\303\243o polinomial ter uma solu\303\247\303\243o em termos de radicais. Infelizmente, ele foi morto com 20 anos de idade em um duelo que pode ter sido encenado a fim de tir\303\241-lo da cena pol\303\255tica, ao mesmo tempo.Uma busca na Internet para "Galois" aparecer\303\241 uma s\303\251rie de dados interessantes sobre a curta vida deste jovem matem\303\241tico extremamente influente.<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Dedu\303\247\303\243o da F\303\263rmula Quadr\303\241tica</Font></Text-field>J\303\241 usamos a f\303\263rmula quadr\303\241tica, sem perceber que temos feito. Sempre que tenham conclu\303\255do o quadrado como uma maneira de resolver uma equa\303\247\303\243o quadr\303\241tica, implementamos a f\303\263rmula quadr\303\241tica de uma forma gradual. Estamos indo agora para formalizar o processo de utiliza\303\247\303\243o de conclus\303\243o do quadrado para resolver a equa\303\247\303\243o geral quadr\303\241tico 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, terminando com a f\303\263rmula quadr\303\241tica, uma f\303\263rmula que d\303\241 a solu\303\247\303\243o para qualquer equa\303\247\303\243o quadr\303\241tica.
EtapasVamos derivar a f\303\263rmula quadr\303\241tica!Solu\303\247\303\243o(1)Subtrair c de ambos os lados da equa\303\247\303\243o.Divida ambos os lados por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUkjbWlHRiQ2JlEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEnJnNkb3Q7RidGMi9GNlEnbm9ybWFsRicvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZOLUklbXN1cEdGJDYlLUYsNiZRInhGJ0YvRjJGNS1GIzYmLUkjbW5HRiQ2JVEiMkYnRjJGPEYvRjJGNS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRjk2LlEiK0YnRjJGPEY+RkBGQkZERkZGSEZKL0ZNUSwwLjIyMjIyMjJlbUYnL0ZQRl5vLUYsNiZRImJGJ0YvRjJGNUY4RlRGam4tRiw2JlEiY0YnRi9GMkY1LUY5Ni5RIj1GJ0YyRjxGPkZARkJGREZGRkhGSi9GTVEsMC4yNzc3Nzc4ZW1GJy9GUEZqby1GWjYlRmluRjJGPEYyRjw=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYyLUkjbWlHRiQ2JlEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEnJnNkb3Q7RidGMi9GNlEnbm9ybWFsRicvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZOLUklbXN1cEdGJDYlLUYsNiZRInhGJ0YvRjJGNS1GIzYmLUkjbW5HRiQ2JVEiMkYnRjJGPEYvRjJGNS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRjk2LlEiK0YnRjJGPEY+RkBGQkZERkZGSEZKL0ZNUSwwLjIyMjIyMjJlbUYnL0ZQRl5vLUYsNiZRImJGJ0YvRjJGNUY4RlRGam4tRiw2JlEiY0YnRi9GMkY1LUY5Ni5RKCZtaW51cztGJ0YyRjxGPkZARkJGREZGRkhGSkZdb0Zfb0Zjby1GOTYuUSI9RidGMkY8Rj5GQEZCRkRGRkZIRkovRk1RLDAuMjc3Nzc3OGVtRicvRlBGXXAtRjk2LlEqJnVtaW51czA7RidGMkY8Rj5GQEZCRkRGRkZIRkpGXW9GX29GY29GMkY8LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYuLUkjbWlHRiQ2JlEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEnJnNkb3Q7RidGMi9GNlEnbm9ybWFsRicvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZOLUklbXN1cEdGJDYlLUYsNiZRInhGJ0YvRjJGNS1GIzYmLUkjbW5HRiQ2JVEiMkYnRjJGPEYvRjJGNS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRjk2LlEiK0YnRjJGPEY+RkBGQkZERkZGSEZKL0ZNUSwwLjIyMjIyMjJlbUYnL0ZQRl5vLUYsNiZRImJGJ0YvRjJGNUY4RlQtRjk2LlEiPUYnRjJGPEY+RkBGQkZERkZGSEZKL0ZNUSwwLjI3Nzc3NzhlbUYnL0ZQRmdvLUY5Ni5RKiZ1bWludXMwO0YnRjJGPEY+RkBGQkZERkZGSEZKRl1vRl9vLUYsNiZRImNGJ0YvRjJGNUYyRjw=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUklbXN1cEdGJDYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtSSNtbkdGJDYlUSIyRidGNS9GOVEnbm9ybWFsRidGNUZBLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIitGJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZaLUkmbWZyYWNHRiQ2KC1GLzYmUSJiRidGMkY1RjgtRiM2JS1GLzYmUSJhRidGMkY1RjhGNUZBLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Znby8lKWJldmVsbGVkR0Y3LUZHNi5RJyZzZG90O0YnRjVGQUZKRkxGTkZQRlJGVEZWL0ZZUSYwLjBlbUYnL0ZmbkZgcEYuLUZHNi5RIj1GJ0Y1RkFGSkZMRk5GUEZSRlRGVi9GWVEsMC4yNzc3Nzc4ZW1GJy9GZm5GZnAtRkc2LlEqJnVtaW51czA7RidGNUZBRkpGTEZORlBGUkZURlZGWEZlbi1GaG42KC1GLzYmUSJjRidGMkY1RjhGXW9GYm9GZW9GaG9Gam9GNUZB(2)Agora vamos usar o m\303\251todo de completar o quadrado. \303\200 esquerda, somar e subtrair o quadrado da metade do coeficiente do termo-x. Assim, somar e subtrair 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(3)Em seguida, adicione 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 para ambos os lados da equa\303\247\303\243o para isolar o quadrado perfeito no lado esquerdo da equa\303\247\303\243o.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(4)Escreva o lado esquerdo da equa\303\247\303\243o como um quadrado perfeito.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(5)Elevar cada lado para a pot\303\252ncia de LUkmbWZyYWNHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KC1JJW1yb3dHRiQ2JS1JI21uR0YkNiVRIjFGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0YyRjUtRiw2JS1GLzYlUSIyRidGMkY1RjJGNS8lLmxpbmV0aGlja25lc3NHRjEvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGQS8lKWJldmVsbGVkR0Y0 (isto \303\251, tirar a raiz quadrada de cada lado) e subtrair 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 de ambos os lados da equa\303\247\303\243o. Escreva este termo como o primeiro termo do lado direito da equa\303\247\303\243o.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(6)Fa\303\247a um denominador comum sob o radical, 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 por 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. Simplificar e expressa como uma fra\303\247\303\243o.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1GOTYuUSomdW1pbnVzMDtGJ0YyRjxGPkZARkJGREZGRkhGSi9GTVEsMC4yMjIyMjIyZW1GJy9GUEZVLUkmbWZyYWNHRiQ2KC1GLDYmUSJiRidGL0YyRjUtRiM2KC1JI21uR0YkNiVRIjJGJ0YyRjwtRjk2LlEnJnNkb3Q7RidGMkY8Rj5GQEZCRkRGRkZIRkovRk1RJjAuMGVtRicvRlBGYW8tRiw2JlEiYUYnRi9GMkY1Ri9GMkY1LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZbcC8lKWJldmVsbGVkR0Y0LUY5Ni5RLCZQbHVzTWludXM7RidGMkY8Rj5GQEZCRkRGRkZIRkpGVEZWLUYjNiYtRiw2I1EhRictSSZtc3FydEdGJDYjLUYjNiUtRlg2KC1GIzYsRlEtRiw2JlEiY0YnRi9GMkY1Rl1vLUZqbjYlUSI0RidGMkY8Rl1vRmNvLUY5Ni5RIitGJ0YyRjxGPkZARkJGREZGRkhGSkZURlYtSSVtc3VwR0YkNiVGWi1GIzYmRmluRi9GMkY1LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YyRjwtRiM2KEZkcUZdby1GW3I2JUZjb0ZdckZfckYvRjJGNUZmb0Zpb0ZccEZecEYyRjxGMkY8RmVwRjJGPA==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1GOTYuUSomdW1pbnVzMDtGJ0YyRjxGPkZARkJGREZGRkhGSi9GTVEsMC4yMjIyMjIyZW1GJy9GUEZVLUkmbWZyYWNHRiQ2KC1GLDYmUSJiRidGL0YyRjUtRiM2KC1JI21uR0YkNiVRIjJGJ0YyRjwtRjk2LlEnJnNkb3Q7RidGMkY8Rj5GQEZCRkRGRkZIRkovRk1RJjAuMGVtRicvRlBGYW8tRiw2JlEiYUYnRi9GMkY1Ri9GMkY1LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZbcC8lKWJldmVsbGVkR0Y0LUY5Ni5RLCZQbHVzTWludXM7RidGMkY8Rj5GQEZCRkRGRkZIRkpGVEZWLUYjNiYtRiw2I1EhRictRlg2KC1JJm1zcXJ0R0YkNiMtRiM2Ky1JJW1zdXBHRiQ2JUZaLUYjNiZGaW5GL0YyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUY5Ni5RKCZtaW51cztGJ0YyRjxGPkZARkJGREZGRkhGSkZURlYtRmpuNiVRIjRGJ0YyRjxGXW9GY29GXW8tRiw2JlEiY0YnRi9GMkY1RjJGPEZnbkZmb0Zpb0ZccEZecEYyRjxGZXBGMkY8LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1JJm1mcmFjR0YkNigtRiM2KS1GOTYuUSomdW1pbnVzMDtGJ0YyRjxGPkZARkJGREZGRkhGSi9GTVEsMC4yMjIyMjIyZW1GJy9GUEZaLUYsNiZRImJGJ0YvRjJGNS1GOTYuUSUmcG07RidGMkY8Rj5GQEZCRkRGRkZIRkpGWUZlbi1GIzYmLUYsNiNRIUYnLUkmbXNxcnRHRiQ2Iy1GIzYrLUklbXN1cEdGJDYlRmZuLUYjNiYtSSNtbkdGJDYlUSIyRidGMkY8Ri9GMkY1LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GOTYuUSgmbWludXM7RidGMkY8Rj5GQEZCRkRGRkZIRkpGWUZlbi1GXHA2JVEiNEYnRjJGPC1GOTYuUScmc2RvdDtGJ0YyRjxGPkZARkJGREZGRkhGSi9GTVEmMC4wZW1GJy9GUEZccS1GLDYmUSJhRidGL0YyRjVGaHAtRiw2JlEiY0YnRi9GMkY1RjJGPEYyRjxGXm9GMkY8LUYjNihGW3BGaHBGXnFGL0YyRjUvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRltyLyUpYmV2ZWxsZWRHRjRGXm9GMkY8
Este resultado \303\251 conhecido como a f\303\263rmula quadr\303\241tica:
A f\303\263rmula quadr\303\241tica As solu\303\247\303\265es para 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 s\303\243o dadas 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
Esta f\303\263rmula pode ter 1, 2, ou mesmo nenhuma resposta real, dependendo se o radicando LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUklbXN1cEdGJDYlLUkjbWlHRiQ2JlEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtSSNtbkdGJDYlUSIyRidGNS9GOVEnbm9ybWFsRidGNUZBLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RKCZtaW51cztGJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZaLUY+NiVRIjRGJ0Y1RkEtRkc2LlEnJnNkb3Q7RidGNUZBRkpGTEZORlBGUkZURlYvRllRJjAuMGVtRicvRmZuRl5vLUYvNiZRImFGJ0YyRjVGOEZqbi1GLzYmUSJjRidGMkY1RjhGNUZB for zero, positivo ou negativo. (Nota: Se o radicando (isto \303\251, discriminante) for negativo, as solu\303\247\303\265es s\303\243o n\303\272meros complexos.)As solu\303\247\303\265es para a equa\303\247\303\243o quadr\303\241tica s\303\243o os valores de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYmUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGNy9GO1Enbm9ybWFsRidGK0Y3Rj0= onde o gr\303\241fico corta o eixo horizontal na fun\303\247\303\243o 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, como mostra o gr\303\241fico abaixo.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JSFHJSFH<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Demonstra\303\247\303\243o</Font></Text-field>Explorar o m\303\251todo usando a f\303\263rmula quadr\303\241tica para encontrar o ponto onde o gr\303\241fico corta o eixo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYmUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGNy9GO1Enbm9ybWFsRidGK0Y3Rj0=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=atrav\303\251s desta demonstra\303\247\303\243o interativa.
MyModule := module ()
export myeq, result;
local a, b, c;
uses DocumentTools;
a, b, c := op(RandomTools:-Generate(list(integer(range = 1 .. 10), 3)));
myeq := a*x^2+b*x+c;
result := convert(map(rhs,ListTools:-Flatten(solve(myeq, [x]))), set);
while nops(select(type, result, realcons))<1 do
a, b, c := op(RandomTools:-Generate(list(integer(range = 1 .. 10), 3)));
myeq := a*x^2+b*x+c;
result := convert(map(rhs,ListTools:-Flatten(solve(myeq, [x]))),set);
end do;
Do(%FuncOut=myeq);
Do(%PlotOut = plot(myeq,x=-10..10, numpoints=200));
Do(%ResOut(caption)="");
end module;
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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=%!G6*-%'CURVESG6$7dw7$$!$+"!""$"$]#!""7$$!1([(\**y%[*)*!#:$"1$*4#e<B\P#!#97$$!1xa4>cN.)*!#:$"2VqoTk$*yE#!#:7$$!1AX!4)HY+(*!#:$"2mGm'>y_\@!#:7$$!1)e<NI))of*!#:$"2y>0#oe^K?!#:7$$!1jC\)*e!Q\*!#:$"1d5.D.>=>!#97$$!0%yc8`B)R*!#9$"2v3l+X%49=!#:7$$!19Fa3vF*H*!#:$"1nYD6UB3<!#97$$!1E^-0_$p>*!#:$"2[&H__N"3g"!#:7$$!1kGd96#\4*!#:$"2&R?P;@#e\"!#:7$$!1'3<M3()**)*)!#:$"2h$pE4r***Q"!#:7$$!1"He;8hv*))!#:$"2Q+LQ]5')H"!#:7$$!1D]+,9^$z)!#:$"2j^c^:vx>"!#:7$$!1/3;KW.*o)!#:$"2%f*)f!R/()4"!#:7$$!1Qyc8:N)e)!#:$"2n-17'pH05!#:7$$!1Z%*)yx@p\)!#:$"1%QckZ0BA*!#:7$$!1tW*)yH?)Q)!#:$"1@$yRQDjD)!#:7$$!1(Qxa*Q5'H)!#:$"1zft!o3lX(!#:7$$!0<Mowq*)=)!#9$"1n7R&3wua'!#:7$$!1u[(\zRT4)!#:$"1%*ozg1)>w&!#:7$$!1BZ%*)=&4!*z!#:$"1F)Rohf3#\!#:7$$!1*)zf>,-"*y!#:$"1_j6rv.ST!#:7$$!1f>Ryck(y(!#:$"2MGT]yfiM$!#;7$$!1$yc8n:Fp(!#:$"1")R[H!\hj#!#:7$$!1a3<M3K!f(!#:$"2jH"G#p./*=!#;7$$!1(RzePhR[(!#:$"1d%>'oo)z8"!#:7$$!1pQxa^P"R(!#:$"1\[</WD9]!#;7$$!1([(\*\z8H(!#:$!2RvwG!*4#o;!#<7$$!1v],.U2)=(!#:$!1=zpg(G=O)!#;7$$!1;JiC,,(3(!#:$!2"yVZ!\o.Z"!#;7$$!1/3;KaA*)p!#:$!1_Is:8`k?!#:7$$!1v],.Al!)o!#:$!23Rk_)G%=q#!#;7$$!20>QwK%4$y'!#;$!1J"oM'fQaK!#:7$$!14=Os/$*ym!#:$!1P8DC:LBQ!#:7$$!1U%)oPDa%e'!#:$!2&*)*y3()R,K%!#;7$$!1\)pRf^8['!#:$!0H.rE%*G%[!#97$$!1X*)ydpD%Q'!#:$!10]Bf(=`J&!#:7$$!20;Kk3lFG'!#;$!1sj;gN)*)y&!#:7$$!1zd:J#QN='!#:$!1$4"3$zg@B'!#:7$$!1Qxa4plzg!#:$!0Nq&Qr-vm!#97$$!1c7D]ogzf!#:$!1,$Q%=n:"3(!#:7$$!1^.297Hxe!#:$!1mUd(pxdZ(!#:7$$!1v],.G#ex&!#:$!1%o"HsLXYy!#:7$$!1$yc8(Qe#o&!#:$!0-]e^6*o")!#97$$!1T$oO`@dd&!#:$!1#*QL[;5<&)!#:7$$!1BY#\eU,[&!#:$!1bEHGz<4))!#:7$$!1hAX!\N#y`!#:$!1<y&G$pY+"*!#:7$$!1\**)zR(p!G&!#:$!1r<yuT")f$*!#:7$$!1NqS")QRs^!#:$!1Y$Roe#\D'*!#:7$$!1\)pR*4hy]!#:$!1wtoB$)fO)*!#:7$$!1Z%*)ydm@(\!#:$!1sM[9#*[05!#97$$!117C[S:v[!#:$!2Fq%=R0TB5!#:7$$!1tY$peP!pZ!#:$!2%p"))*="e3/"!#:7$$!1yc8FqZxY!#:$!2.Mqx[-T0"!#:7$$!2&Hf=P-?tX!#;$!2$***3)[T9n5!#:7$$!1^,.1SZsW!#:$!2Bei8$onx5!#:7$$!2:U%)od8=P%!#;$!27W/kYvh3"!#:7$$!1#['HfM_rU!#:$!2s;06]FE4"!#:7$$!1JjE`g<vT!#:$!2K?O]LJp4"!#:7$$!1%*)yd&>-rS!#:$!2Utz")e&\*4"!#:7$$!1=Pu[bvrR!#:$!2KK(4D-#**4"!#:7$$!21C['HBGnQ!#;$!2,k(*>gQ#)4"!#:7$$!2PrU&3*3Fx$!#;$!2bTuf(Q$[4"!#:7$$!2kMpQd(=oO!#;$!2*GlQ^+**)3"!#:7$$!2&=Pu[V2oN!#;$!2PoyJ-W83"!#:7$$!2/05?![?oM!#;$!1$[RnQ><2"!#97$$!1LoOt1*QO$!#:$!0.dC\O&f5!#87$$!1>Qw_N"yE$!#:$!1m$[1I!RY5!#97$$!2$zf>RuTpJ!#;$!2N#)o4E85."!#:7$$!2W&4>QkxgI!#;$!2HF%45fy65!#:7$$!1kFb54TiH!#:$!1b+Y"))3M#**!#:7$$!1T$oOt8='G!#:$!1)*R8B?`/(*!#:7$$!1**)zf**3&fF!#:$!1-_%*o?=h%*!#:7$$!1a3<M5ZlE!#:$!0*HORC.>#*!#97$$!21Ig?hH_c#!#;$!1k8*Q$RVT*)!#:7$$!2V&3<M7vlC!#;$!1W<bC23Y')!#:7$$!2aGd9HS$fB!#;$!1OXw?dB3$)!#:7$$!116AWsVlA!#:$!2'GZEY?H"*z!#;7$$!2v_06i#4d@!#;$!11j"GR#p.w!#:7$$!1%ze<&*>$f?!#:$!0^e.&4wLs!#97$$!20:Ig+zD'>!#;$!164L$p:*[o!#:7$$!2sFb5T^&e=!#;$!1bm!4%z>9k!#:7$$!1v],.I5a<!#:$!1'4M*ym%f&f!#:7$$!2uU&3</2f;!#;$!11a$yo[+_&!#:7$$!2L!3;K+:e:!#;$!19PcM(ot.&!#:7$$!2()******fh'f9!#;$!1Ma[83oYX!#:7$$!17D]+"**GN"!#:$!2/fzy#o&G*R!#;7$$!2<Qw_&)>0E"!#;$!2F1lm`[_\$!#;7$$!21MoO$*=W:"!#;$!2nxM\RoE!H!#;7$$!2cBZ%*[yY0"!#;$!1#=v%*>"3DB!#:7$$!1xsX"H9!f&*!#;$!2n(H#4*QYL<!#;7$$!1Jxa4zXq&)!#;$!2<*[%)R)Q=7"!#;7$$!1rV([(H>iv!#;$!1P52Sv')yZ!#;7$$!1*)e<N!\M\'!#;$"2#eb$ev&*)oA!#<7$$!1Hu[(\:N^&!#;$"1pR?M8wJ*)!#;7$$!1l;Lm_>YX!#;$"1K3$4qA(p:!#:7$$!1&['Hfe97N!#;$"2jaKz*\j8B!#;7$$!2B=Pu[Z.[#!#<$"2LhMmCVs2$!#;7$$!1$Rze<ZUb"!#;$"2jxL@5f2y$!#;7$$!1HJkGd9sX!#<$"1X\O$z=jj%!#:7$$"1R#f=P9tg%!#<$"1`3K%)yqq`!#:7$$"2C/5?SsV`"!#<$"1N&)G34/^i!#:7$$"2aLnMpe!fD!#<$"1w*R(oZt7r!#:7$$"1Lu[(\")RZ$!#;$"1'zQCnq)**y!#:7$$".(Rzy!H]%!#8$"1c4A(4)30))!#:7$$"1UjE`YlQb!#;$"1iXHw1pP(*!#:7$$"1$f<Nqy%pl!#;$"2'ytrYjro5!#:7$$"1AQw_X=Dv!#;$"24Eun;V'e6!#:7$$"1#3:IgiZ^)!#;$"22"pU!>#o`7!#:7$$"1Y4>Qc=Q&*!#;$"2x'QKO=.a8!#:7$$"2wNrUlKe0"!#;$"1c'*z#QWhX"!#97$$"2h8Faom2;"!#;$"1f99y7Nj:!#97$$"2#Hf=PE>`7!#;$"1Y%Q$)G.'f;!#97$$"2n>RyOUsN"!#;$"2B8x(yX+q<!#:7$$"2wT$oO$><Y"!#;$"2`:q7"y.$)=!#:7$$"2PQw_D-Cc"!#;$"0Q]\)=.%*>!#87$$"2Xxa4*>$Ql"!#;$"1jV>=;e'4#!#97$$"2#\(\**y]Dw"!#;$"2y/v1;*p?A!#:7$$"2L$oOt)\Y&=!#;$"2wUrR^#pFB!#:7$$"2805?+$yh>!#;$"2xf0jl&GaC!#:7$$"2lMpQ(Rhc?!#;$"1Wp%GGd#oD!#97$$"1(\**)z&e1;#!#:$"1H*3QTr`p#!#97$$"23BY#\OtfA!#;$"2Nb]f`E%=G!#:7$$"27E_/43JO#!#;$"2A!z2dW"*[H!#:7$$"2(Qu[(4Q!eC!#;$"2y"*fogD12$!#:7$$"2&oLnMHVgD!#;$"1-Z.H!GR?$!#97$$"2V#['HR#zmE!#;$"2YO*3"37YM$!#:7$$"2ONqShy$fF!#;$"2c;N[#*>*oM!#:7$$"1MnMpUPfG!#:$"2Yg(pO:50O!#:7$$"1X"HeczE'H!#:$"1t9kt1*yu$!#97$$"2s5@UkVP1$!#;$"14u7Fuk*)Q!#97$$"2xT$oO$G:;$!#;$"1c>r6)[(GS!#97$$"2v9Hec,,F$!#;$"1UruxwV&=%!#97$$"2(Hg?T%fwO$!#;$"1N#fTcS#GV!#97$$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Digite o valor de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYoUSJ4RicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR0Y2LyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRLGJvbGQtaXRhbGljRicvJStmb250d2VpZ2h0R1ElYm9sZEYnRjRGOS9GPUZBRj9GK0Y0RjlGQkY/ onde o gr\303\241fico corta o eixo horizontal para a fun\303\247\303\243o quadr\303\241tica na forma exata (sem decimais):LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LlEifkYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRS1JI21pR0YkNiZRInhGJy8lJ2l0YWxpY0dRJXRydWVGJ0YvL0YzUSdpdGFsaWNGJy1GLDYuUSI9RidGL0YyRjVGN0Y5RjtGPUY/RkEvRkRRLDAuMjc3Nzc3OGVtRicvRkdGVUYvRjI= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTkYyRjw=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=use DocumentTools in
try
Do(%ResOut(caption)="");
if evalb(Do({%XInterIn1,%XInterIn2})=MyModule:-result) then
Do(%ResOut(caption)="Correct");
else
if has(evalf(MyModule:-result), evalf(DocumentTools:-Do(%XInterIn1))) then
Do(%ResOut(caption)="Sua primeira resposta \303\251 correta. Sua segunda \303\251 incorreta.");
elif has(evalf(MyModule:-result), evalf(DocumentTools:-Do(%XInterIn2))) then
Do(%ResOut(caption)="Sua segunda resposta \303\251 correta. Sua primeira \303\251 incorreta.");
else
Do(%ResOut(caption)="Suas duas respostas est\303\243o incorretas. Tente novamente.");
end if;
end if;
catch "`%1` n\303\243o \303\251 avaliada para um m\303\263dulo":
Do(%ResOut(caption)="Por favor clique no bot\303\243o para uma fun\303\247\303\243o antes de verificar suas respostas");
catch "entrada inv\303\241lida: %1 est\303\241 esperando por %2 argumentos, mas recebeu %3":
Do(%ResOut(caption)="Por favor insira uma resposta na caixa \303\240 esquerda antes de checar suas respostas");
end try;
end use;
use DocumentTools in
Do(%PlotOut=PLOT());
Do(%ResOut(caption)="");
seq(SetProperty(i,value,NULL),i in [XInterIn1, XInterIn2, FuncOut]);
end use;
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFH