A quadratic equation has equal roots if and only if the discriminant
[tex]\Delta = b^2-4ac[/tex]
is zero.
So, we have to impose
[tex](3p)^2-4p=0 \iff 9p^2-4p=0 \iff p(9p-4)=0 \iff p=0 \lor\; p=\dfrac{4}{9}[/tex]
Since p is non-zero, the only possible value for p is 4/9.
