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

Jun 10, 2016

Zeros of $y = - {x}^{2} - x + 5$ are

$\frac{- 1 - \sqrt{21}}{2}$ and $\frac{- 1 + \sqrt{21}}{2}$

#### Explanation:

Quadratic formula gives the roots or zeros of general form of quadratic equation $a {x}^{2} + b x + c$ as $\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

Hence zeros of $y = - {x}^{2} - x + 5$ are

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

$\frac{1 \pm \sqrt{1 + 20}}{- 2}$ or

$\frac{- 1 \pm \sqrt{21}}{2}$ or

i.e. $\frac{- 1 - \sqrt{21}}{2}$ and $\frac{- 1 + \sqrt{21}}{2}$