The set of values of p for which the roots of the equation $3x^2+2x+p(p-1)=0$ are of opposite sign is :

$\text{ Roots of }f\left(x\right)=3x^2+2x+p(p-1)=0$ are opposite are sign
(a) Roots are real and distinct

$f\left(0\right)<0$
$\begin{array}{r}\therefore p(p-1)<0\\ \Rightarrow 0<p<1\end{array}$
$D=4-12p(p-1)>0\text{ as }p(p-1)<0.$
Set of values of p is (0, 1).