Finding integral roots of $x^2 + px + q = 0$ if $p+q=198$.

Question

Given the relation that $p+q=198$, the question is to find all the integral roots of the equation: $$ x^2+px + q = 0 $$

How to proceed?

I know we'll have to use Vieta's formulas, but I don't know how to. Hints?

Answer 1

HINT:

If the roots are $a,b$

using Vieta's formula $a+b=-p$ and $q=ab$

So,we have $-(a+b)+ab=198\iff (a-1)(b-1)=199$ which is prime