Solve : $f (x) = (x^{3} - 2 x^{2} - 5 x + 6) < 0$

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Solution

$f (x) = (x^{3} - 2 x^{2} - 5 x + 6) < 0$ factors of $f (x) = x^{3} - 2 x^{2} - 5 x + 6$ are $x = 1, - 2, 3$

So, $f (x) = x^{3} - 2 x^{2} - 5 x + 6 = (x - 1) (x + 2) (x - 3) = 0.$

As it is given that f(x) is less than 0, then $x = - 2$ which is < 0.

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f (x) = x^{3} + 2 x^{2} - 5 x - 6

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Factorise: $x^{3} - 2 x^{2} - 5 x + 6$

x = [- 2, 3]

f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} \frac{x^{3} - 2 x^{2} - 5 x + 6}{x - 1}, & i f x \neq 1 - 6 & i f x = 1 \end{matrix}

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