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Inequalities Involving Modulus Function

Solve the fol...

Question

Solve the following inequality:
$\frac{1 - 2 x - 3 x^{2}}{3 x - x^{2} - 5} > 0$

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Solution

$\frac{1 - 2 x - 3 x^{2}}{3 x - x^{2} - 5} > 0$
$\frac{3 x^{2} + 2 x - 1}{x^{2} - 3 x + 5} > 0$
As discriminant of $x^{2} - 3 x + 5$ less than $0$ .
$x^{2} - 3 x + 5 > 0 \forall x ϵ R$
$3 x^{2} + 2 x - 1 > 0$
$3 x^{2} + 3 x - x - 1 > 0$
$(3 x - 1) (x + 1) > 0$
$x ϵ (- \infty, - 1) \cup (\frac{1}{3}, \infty)$

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Inequalities Involving Modulus Function

Standard IX Mathematics

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