# Math Help - root of the equation

1. ## root of the equation

(p^2)(x^2)-12x+p+7=0 has the root 3/2..find the value of p.

3. To explain HallsOfIvy's solution, remember that the roots of an equation are the values of $x$ when $y = 0$. Here, you are given an equation in the form $y = f(x)$ with $y = 0$ and $f(x) = (p^2)(x^2)-12x+p+7$ for some $p$. Since you are given that one root is $\frac{3}{2}$, you know that when $y = 0$ (which is our case), $x = \frac{3}{2}$. So you can just substitute $x = \frac{3}{2}$ into $f(x)$ and solve for $p$, to find which values of $p$ (there may be more than one) satisfy the equation $f(x) = 0$ when $x = \frac{3}{2}$.