# How do you find the roots, real and imaginary, of y= -2x^2 + 15x + 22  using the quadratic formula?

Jan 18, 2016

at $y = 0$ $\textcolor{w h i t e}{\ldots \ldots \ldots} x = + 8.756 \text{ or } - 1.256$

#### Explanation:

Given: $\textcolor{w h i t e}{\ldots} \textcolor{b r o w n}{y = - 2 {x}^{2} + 15 x + 22}$

Using standard for of $y = a {x}^{2} + b x + c = 0$

Where: $\textcolor{w h i t e}{\ldots .} x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$a = - 2$
$b = 15$
$c = 22$

Thus: $\textcolor{w h i t e}{\ldots . .} x = \frac{- 15 \pm \sqrt{{15}^{2} - 4 \left(- 2\right) \left(22\right)}}{2 \left(- 2\right)}$

$x = \frac{- 15 \pm \sqrt{225 + 176}}{- 4}$

$x = \frac{- 15 \pm \sqrt{401}}{- 4}$

But 401 is a prime number so unable to break it down further

Using $\sqrt{401} = 20.025$ to 3 decimal places

$x = + 8.756 \text{ or } - 1.256$