Specimen Cyprus Seniors Provincial/2nd grade/Problem 3
Prove that if are positive integers, then the equation has irrational roots.
Note that the square root of the discriminant of the quadratic is:
Since is a positive integer:
So, is a non-perfect square, and thus, is irrational.
Since and are integers, the square root of the discriminant: is irrational.
Therefore, the quadratic: has irrational roots.