# How do you find the roots, real and imaginary, of y=-2(x +1 )^2-x+1 using the quadratic formula?

Feb 19, 2018

The roots are:
$\frac{5 + \sqrt{17}}{- 4} , \mathmr{and} \frac{5 - \sqrt{17}}{- 4}$

#### Explanation:

First, expand the equation:

$- 2 \left({x}^{2} + 2 x + 1\right) - x + 1$

$- 2 {x}^{2} - 4 x - 2 - x + 1$

$- 2 {x}^{2} - 5 x - 1$

Now that it is in $a {x}^{2} + b x + c$ standard form, with

$a = - 2 , b = - 5 , c = - 1$,

you can plug into the quadratic formula:

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

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

$\frac{5 \pm \sqrt{17}}{- 4}$

$\frac{5 + \sqrt{17}}{- 4} , \mathmr{and} \frac{5 - \sqrt{17}}{- 4}$