# How do I solve this ?

## Given p-2 is one of the roots of the quadratic equation ${x}^{2}$ - m$x$ + 9 $- {p}^{2}$ = 0 . Express p in terms of m.

Aug 27, 2017

$p = \frac{2 m + 13}{m + 4}$

#### Explanation:

$p - 2$ is a root of $f \left(x\right) = {x}^{2} - m x + 9 - {p}^{2}$.

So ${\left(p - 2\right)}^{2} - m \left(p - 2\right) + 9 - {p}^{2} = 0$.

Let's expand the parentheses:

$R i g h t a r r o w {p}^{2} - 4 p + 4 - m p + 2 m + 9 - {p}^{2} = 0$

Then, let's simplify the equation:

$R i g h t a r r o w {p}^{2} - {p}^{2} - 4 p - m p + 2 m + 9 + 4 = 0$

$R i g h t a r r o w - p \left(4 + m\right) + 2 m + 13 = 0$

Now, let's solve for $p$:

$R i g h t a r r o w - p \left(4 + m\right) = - \left(2 m + 13\right)$

$R i g h t a r r o w - p = - \frac{2 m + 13}{4 + m}$

$\therefore p = \frac{2 m + 13}{m + 4}$