First slide

Theory of equations

Question

The value of ‘a’ for which the equation $3 x^{2} + 2 (a^{2} + 1) x + (a^{2} - 3 a + 2) = 0$ has roots of opposite sign, lies in

Easy

A

(1, 2)
B

$(- \infty, 1)$
C

$(2, \infty)$
D

$(- \infty, \infty)$

Solution

Roots are of opposite .sign $\Rightarrow \frac{c}{a} < 0 \Rightarrow a c < 0$
                                                     $\Rightarrow 3 (a^{2} - 3 a + 2) < 0$

                                                     $\Rightarrow a^{2} - 3 a + 2 < 0$

                                                     $\Rightarrow a \in (1, 2)$

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