Find a nonzero $p$ such that $px^2-12x+4=0$ has only one solution.
I know that a quadratic equation has only one solution when its discriminant, which is the part under the square root in the quadratic formula, is zero. So I want to find $p$ such that the discriminant of $px^2-12x+4=0$ is zero. The discriminant is $b^2-4ac$, where $a, b, c$ are the coefficients of the quadratic equation. In this case, $a=p$, $b=-12$, and $c=4$. So I need to solve $(-12)^2-4p(4)=0$ for $p$. Simplifying, I get $144-16p=0$. Dividing both sides by 16, I get $9-p=0$. Adding $p$ to both sides, I get $p=9$. This is a nonzero value of $p$ that makes the discriminant zero, so it should be the answer. To check, I can plug in $p=9$ into the original equation and see if it has only one solution. I get $9x^2-12x+4=0$. Factoring, I get $(3x-2)(3x-2)=0$. This has only one solution, $x=\frac{2}{3}$, since both factors are the same. So I have verified that $p=9$ is the correct answer. 