Question

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

Answer 1

Products of the roots is negative
$\Rightarrow \frac{(p-1)p}{3}<0$
$\Rightarrow (p-0)(p-1)<0$ i.e $0<p<1$
Hence the set of values are (0,1)