How do you find the zeros, real and imaginary, of y=- 5x^2-2x+10  using the quadratic formula?

Jul 21, 2016

$x = \frac{- 1 \pm \sqrt{51}}{5}$

Explanation:

$y = - 5 {x}^{2} - 2 x + 10 = 0$
Use the new improved quadratic formula (Socratic Search)
$D = {d}^{2} = {b}^{2} - 4 a c = 4 + 200 = 204 = 4 \left(51\right)$ --> $d = \pm 2 \sqrt{51}$
There are 2 real roots:
$x = - \frac{b}{2 a} \pm \frac{d}{2 a} = \frac{2}{-} 10 \pm \frac{2 \sqrt{51}}{-} 10 = - \frac{1}{5} \pm \frac{\sqrt{51}}{5} =$
$x = \frac{- 1 \pm \sqrt{51}}{5}$