The number of all possible positive integral values of for which the roots of 6x^2-11x+=0 …

Question

The number of all possible positive integral values of $\alpha$ for which the roots of $6x^2-11x+\alpha=0$ are rational numbers is:

Accepted Answer

$D=121-24\alpha$ must be a perfect square. Testing positive integers, $\alpha=3,4,5$ work, giving 3 values.

Solutions · 1