Question

Quais são as raízes da equação x² + 10x +16 = 0?

2 e 8
-2 e -8
5 e -5
-16 e - 4

Answer 1

Determinar as raízes

$\sf x^2 + 10x + 16 = 0$

coeficientes: a = 1, b = 10, c = 16

$\sf \Delta = b^2 - 4ac$

$\sf \Delta = (10)^2 - 4*(1)*(16)$

$\sf \Delta = 100 - 64$

$\sf \Delta = 36$

$\sf x = \dfrac{- b \pm \sqrt{\Delta}}{2a}$

$\sf x = \dfrac{- (10) \pm \sqrt{36}}{2*(1)}$

$\sf x = \dfrac{-10 \pm 6}{2}$

•$~~\sf x' = \dfrac{-10 + 6}{2} = - \dfrac{4}{2} = - 2$

•$~~\sf x'' = \dfrac{- 10 - 6}{2} = - \dfrac{16}{2} = - 8$

$\sf S = \left\{- 8~~;~~- 2\right\}$

Raízes -8 e -2

Answer 2

Resposta:

-2 e -8

Explicação passo-a-passo:

${x}^{2} + 10x + 16 = 0$

$x = \frac{ - 10± \sqrt{ {10}^{2} - 4 \times 1 \times 16} }{2 \times 1}$

$x = \frac{ - 10± \sqrt{ {10}^{2} - 4 \times 16} }{2 \times 1}$

$x = \frac{ - 10± \sqrt{ {10}^{2} - 4 \times 16 } }{2}$

$x = \frac{ - 10± \sqrt{100 - 4 \times 16} }{2}$

$x = \frac{ - 10± \sqrt{100 - 64} }{2}$

$x = \frac{ - 10± \sqrt{36} }{2}$

$x = \frac{ - 10±6}{2}$

$x = \frac{ - 10 + 6}{2} \\ x = \frac{ - 10 - 6}{2}$

$x = - 2 \\ x = - 8$

$\boxed{ x_{1} = - 8 } \: \: \boxed{ x_{2} = - 2}$