# How do you find the roots, real and imaginary, of y= -3x^2-16x +8  using the quadratic formula?

Oct 22, 2017

Roots are $\ast 5.7936 , - 0.4603 \ast$

#### Explanation:

Standard form of equation is $a {x}^{2} + b x + c = 0$
Roots are$= \frac{\left(- b\right) \pm \sqrt{{b}^{2} - \left(4 a c\right)}}{2 a}$

Given equation is $- 3 {x}^{2} - 16 x + 8 = 0$
$a = - 3 , b = - 16 , c = 8$

$x = \frac{- \left(- 16\right) \pm \sqrt{{\left(- 16\right)}^{2} - \left(4 \cdot \left(- 3\right) 8\right)}}{2 \cdot \left(- 3\right)}$

$x = \frac{16 \pm \sqrt{256 + 96}}{6}$

$x = \frac{16 \pm \sqrt{352}}{6}$

$x = 5.7936 , - 0.4603$