First slide

Theory of equations

Question

Suppose $p \in R$ . If the roots of $3 x^{2} + 2 x +$ $p (1 - p) = 0$ are of opposite signs, then $p$ must lie in the interval

Moderate

A

$(- \infty, 0)$
B

(0, 1)
C

$(1, \infty)$
D

$(2, \infty)$

Solution

We must have $\frac{1}{3} p (1 - p) < 0$
$p (1 - p) < 0 \Rightarrow 0 < p < 1$ .

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