Question

1º) A equação de segundo grau 10 x² + 72 x - 64 = 0 tem por solução? *

a) x‘ = -8 e x’’ = -4/5

b) x‘ = 8 e x’’ = 4/5

c) x‘ = 8 e x’’ = -4/5

d) x‘ = -8 e x’’ = 4/5

​

Answer 1

Resposta: D - X2 = -8 e X1 = 4/5

Explicação passo-a-passo:

eq. 2o grau:  ax^2 + bx + c = 0

Sendo a = 10

b = 72

c = -64

Calculando o Delta:

$Delta = b^{2} - 4*a*c\\Delta = 72^2 - 4*10*(-64)\\Delta = 5184 - (-2560)\\Delta = 5184 + 2560\\Delta = 7744$

Calculando as raízes:

$X1 = \frac{-b + \sqrt{Delta}}{2a}\\X1 = \frac{-72 + \sqrt{7744}}{2*10}\\\\X1 = \frac{-72 + 88}{20}\\\\X1 = \frac{16}{20}\\X1 = \frac{4}{5}$

$X2 = \frac{-b + \sqrt{Delta}}{2a}\\X2 = \frac{-72 - \sqrt{7744}}{2*10}\\\\X2 = \frac{-72 - 88}{20}\\\\X2 = \frac{160}{20}\\X2 = -8$

Answer 2

$10x^2+72x-64=0\\\\\\x_{1,\:2}=\frac{-72\pm \sqrt{72^2-4\cdot \:10\left(-64\right)}}{2\cdot \:10}= 88\\\\x_{1,\:2}=\frac{-72\pm \:88}{2\cdot \:10}\\\\x_1=\frac{-72+88}{2\cdot \:10},\:x_2=\frac{-72-88}{2\cdot \:10}\\\\\frac{-72+88}{2\cdot \:10}= \frac{4}{5} \\\\\frac{-72-88}{2\cdot \:10} = -8\\\\\frac{16}{2\cdot \:10}=\frac{4}{5} \\\\\\-\frac{160}{20}=-8$

Letra d.

x‘ = -8 e x’’ = 4/5

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