First slide

Theory of expressions

Question

The value of k for which the equation $3 x^{2} + 2 x (k^{2} + 1) + k^{2} - 3 k + 2 = 0$ has roots of opposite signs, lies in the interval

Moderate

A

$(- \infty, 0)$
B

$(- \infty, - 1)$
C

$(1, 2)$
D

$(3 / 2, 2)$

Solution

It is given that the roots are of opposite signs.
$∴$ Product of roots $< 0$
$\Rightarrow \frac{k^{2} - 3 k + 2}{3} < 0 \Rightarrow k^{2} - 3 k + 2 < 0 \Rightarrow k \in (1, 2)$

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