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

Feb 18, 2016

Roots are complex conjugate pair $x = \frac{5 + i \sqrt{15}}{10}$ and $\frac{5 - i \sqrt{15}}{10}$

#### Explanation:

By finding the roots, real and imaginary, of y=−5x^2+5x−2, means finding zeros of the function y=−5x^2+5x−2 or solving the equation −5x^2+5x−2=0.

The solution of equation $a {x}^{2} + b x + c = 0$ are given by $x = \left(\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}\right)$.

As $a = - 5 , b = 5 \mathmr{and} c = - 2$,

$x = \left(\frac{- 5 \pm \sqrt{{\left(- 5\right)}^{2} - 4 \cdot \left(- 5\right) \cdot \left(- 2\right)}}{2 \left(- 5\right)}\right)$.or

$x = \left(\frac{- 5 \pm \sqrt{25 - 40}}{- 10}\right)$ or

$x = \left(\frac{5 \pm \sqrt{- 15}}{10}\right)$ or

$x = \left(\frac{5 \pm i \sqrt{15}}{10}\right)$

Hence, roots are complex conjugate pair $\frac{5 + i \sqrt{15}}{10}$ and $x = \frac{5 - i \sqrt{15}}{10}$