Question

1. Fatorando os polinômios, encontre as raízes das equações abaixo:

a) x² - 64 = 0
b) x² + 12x = 0
c) 2x² - 14x = 0​

Answer 1

Resposta:

a) x=8, x=-8

b) x=0, x=-12

c) x=7, x=0

Explicação passo a passo:

a) $x^2-64=0$

$x^2=64$

$x=\sqrt{64},\:x=-\sqrt{64}$

$x=8,\:x=-8$

b) $x^2+12x=0$

$x_{1,\:2}=\frac{-12\pm \sqrt{12^2-4\cdot \:1\cdot \:0}}{2\cdot \:1}$

$x_{1,\:2}=\frac{-12\pm \:12}{2\cdot \:1}$

$x_1=\frac{-12+12}{2\cdot \:1},\:x_2=\frac{-12-12}{2\cdot \:1}$

$x_1=\frac{-12+12}{2\cdot \:1}=\frac{0}{2\cdot \:1}=\frac{0}{2}=0$

$x_2=\frac{-12-12}{2\cdot \:1}=\frac{-24}{2\cdot \:1}=\frac{-24}{2}=-\frac{24}{2}=-12$

$x=0,\:x=-12$

c) $2x^2-14x=0$

$x_{1,\:2}=\frac{-\left(-14\right)\pm \sqrt{\left(-14\right)^2-4\cdot \:2\cdot \:0}}{2\cdot \:2}$

$x_{1,\:2}=\frac{-\left(-14\right)\pm \:14}{2\cdot \:2}$

$x_1=\frac{-\left(-14\right)+14}{2\cdot \:2},\:x_2=\frac{-\left(-14\right)-14}{2\cdot \:2}$

$x_1=\frac{-\left(-14\right)+14}{2\cdot \:2}=\frac{14+14}{2\cdot \:2}=\frac{28}{2\cdot \:2}=\frac{28}{4}=7$

$x_2=\frac{-\left(-14\right)-14}{2\cdot \:2}=\frac{14-14}{2\cdot \:2}=\frac{0}{2\cdot \:2}=\frac{0}{4}=0$

$x=7,\:x=0$