Let $\displaystyle p$ be a prime. How do we show that the number of reducible polynomials over $\displaystyle \mathbb{Z}_p$ of the form $\displaystyle x^2+ax+b$ is $\displaystyle p(p+1)/2$?

I just know that $\displaystyle \mathbb{Z}_p$ is a field, and a polynomial of the form $\displaystyle x^2+ax+b$ is of degree 2, so there is a theorem which says a polynomial of degree 2 or 3 is reducible over a field if and only if it has a root in that field.

So how can I show the total number of polynomials $\displaystyle x^2+ax+b$ which have a zero in $\displaystyle \mathbb{Z}_p$ is $\displaystyle p(p+1)/2$? Any help would be appreciated.