Question

1) sendo f(x)= -2x² + 3x - 8 uma função função 2° grau , determinando os seus coeficientes obteremos ?

​

Answer 1

Resposta:

$x_1=\frac{3}{4}-\frac{\sqrt{55}}{4},\:x_2=\frac{3}{4}+\frac{\sqrt{55}}{4}$

Explicação passo-a-passo:

$f\left(x\right)=\:-2x^2\:+\:3x\:-\:8$

$-2x^2+3x-8=0$

$x_{1,\:2}=\frac{-3\pm \sqrt{3^2-4\left(-2\right)\left(-8\right)}}{2\left(-2\right)}\\x_{1,\:2}=\frac{-3\pm \sqrt{55}i}{2\left(-2\right)}\\x_1=\frac{-3+\sqrt{55}i}{2\left(-2\right)},\:x_2=\frac{-3-\sqrt{55}i}{2\left(-2\right)}$

$x_1=\frac{-3+\sqrt{55}}{2\left(-2\right)}=\frac{-3+\sqrt{55}}{-2\cdot \:2}=\frac{-3+\sqrt{55}}{-4}=-\frac{-3+\sqrt{55}}{4}=\frac{3}{4}-\frac{\sqrt{55}}{4}$

$x_2=\frac{-3-\sqrt{55}}{2\left(-2\right)}=\frac{-3-\sqrt{55}}{-2\cdot \:2}=\frac{-3-\sqrt{55}}{-4}=-\frac{-3-\sqrt{55}}{4}=\frac{3}{4}+\frac{\sqrt{55}}{4}i$

$x_1=\frac{3}{4}-\frac{\sqrt{55}}{4},\:x_2=\frac{3}{4}+\frac{\sqrt{55}}{4}$