Question

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

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

Answer 1

Answer: (B)

$(0,1)$

Given equation
$3x^2+2x+p(p-1)=0$
Since, roots are of opposite sign.
$\Rightarrow \alpha \beta <0$
$\frac{p(p-1)}{3}<0$
$\Rightarrow p(p-1)<0$
$0<p<1$
$\Rightarrow p\in (0,1)$.