First slide

Theory of expressions

Question

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

Moderate

A

$(- \infty, 0)$
B

$(0, 1)$
C

$(1, \infty)$
D

$(0, \infty)$

Solution

The given equation is $3 x^{2} + 2 x + p (p - 1) = 0$
The Roots of given equation are of opposite signs

$\Rightarrow$ Product of roots $< 0$

$\Rightarrow \frac{constant term}{coeff . of x^{2}} < 0$

$\Rightarrow \frac{p (p - 1)}{3} < 0$

$\Rightarrow (P - 0) (P - 1) < 0$

$\Rightarrow 0 < P < 1.$

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