# How do you find the roots, real and imaginary, of y=-5x^2 +x -4  using the quadratic formula?

Jul 16, 2017

#### Answer:

See a solution process below:

#### Explanation:

The quadratic formula states:

For $a {x}^{2} + b x + c = 0$, the values of $x$ which are the solutions to the equation are given by:

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

Substituting $- 5$ for $a$; $1$ for $b$ and $- 4$ for $c$ gives:

$x = \frac{- 1 \pm \sqrt{{1}^{2} - \left(4 \cdot - 5 \cdot - 4\right)}}{2 \cdot - 5}$

$x = \frac{- 1 \pm \sqrt{1 - \left(80\right)}}{- 10}$

$x = \frac{- 1 \pm \sqrt{- 79}}{- 10}$

$x = \frac{- 1 + \sqrt{- 79}}{- 10}$ and $x = \frac{- 1 - \sqrt{- 79}}{- 10}$