Question

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

• A. $(-1,-\infty )$
• B. $(-\infty ,\infty )$
• C. $(2,6)$
• D. $(0,1)$

Answer 1

The correct option is D $(0,1)$

Let the $\alpha$ and $\beta$ be the roots of given equation
$\alpha \beta$ $=$ $\frac{p(p-1)}{3}$.
Since the roots are of opposite sign, therefore $\alpha \beta <0$
$\frac{p(p-1)}{3}<0$
$\therefore p$ has value $(0,1)$.