Question

The equation x2+3px+p=0, where p is non-zero constant, has equal roots. Find the value of p

Answer 1

A quadratic equation has equal roots if and only if the discriminant

$\Delta = b^2-4ac$

is zero.

So, we have to impose

$(3p)^2-4p=0 \iff 9p^2-4p=0 \iff p(9p-4)=0 \iff p=0 \lor\; p=\dfrac{4}{9}$

Since p is non-zero, the only possible value for p is 4/9.