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

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

Roots are of opposite sign means that the product of roots should be negative.
Hence, $\frac{p(p-1)}{3}<0$
$\Rightarrow p(p-1)<0p^2-p<0.$
This happens for 0 < p < 1.