Consider a quadratic equation;
$$ x^2 + 7x – 14(a^2 + 1) = 0,$$
… (where $a$ is an integer)
For how many different value of $a$, the equation will have at least one integer root?
I found out its discriminant, it comes out to be
$$ (49 + 56(a^2+1))^{1/2}. $$ This should be the perfect square and also odd so that the at least one root be integer.
But I am unable to get the values.
How I can achieve this ?
Thanks in advance.