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Definition of Functions

Solve the fol...

Question

Solve the following inequality:
$\frac{1 + 3 x^{2}}{2 x^{2} - 21 x + 40} < 0$

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Solution

$\frac{1 + 3 x^{2}}{2 x^{2} - 21 x + 40} < 0$
As $1 + 3 x^{2} > 0 \forall x ϵ R$
$\frac{1}{2 x^{2} - 21 x + 40} < 0$
$\frac{1}{2 x^{2} - 16 x - 5 x + 40} < 0$
$\frac{1}{(2 x - 5) (x - 8)} < 0$
$x ϵ (\frac{5}{2}, 8)$

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