TITLE: Is it possible for a quadratic equation to have one rational root and one irrational root.
QUESTION [7 upvotes]: Is it possible for a quadratic equation  with rational coefficients to have one rational root and one irrational root?
I have seen that there is a post about this, but I dont understand it. 
How can it be shown using quadratic formula?

REPLY [6 votes]: Suppose $ax^2+bx+c=a(x-p)(x-q)$ with $a,b,c,p$ rational. Then by expanding and comparing coefficients, you see that $q=-p-\dfrac{b}{a}$. So what can you say about $q$?