# Integer Coefficient Quadratic polynomials with common nonrational zeros

I am learning about polynomials from Barbeau's book and I was hoping for a hint on a question which is as follows:

Let $p(t)$ and $q(t)$ be two quadratic polynomials with integer coefficients. Prove that, if they have a nonrational zero in common, then on must be a constant multiple of the other.

A hint is appreciated.

If a quadratic polynomial with integer coefficients has an irrational zero $\alpha=a+\sqrt{b}$, then the conjugate of $\alpha$, i.e. $a-\sqrt{b}$ is also a zero. Therefore $p(t)$ and $q(t)$ share common roots and thus one must be a constant multiple of another.