First slide

Theory of equations

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

Easy

A

$(- \infty, 0)$
B

$(0,1)$
C

$(1, \infty)$
D

$(0, \infty)$

Solution

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

$\Rightarrow p \in (0, 1)$

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