Find the roots of $x^{3} - 23 x^{2} + 142 x - 120 = 0$

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Solution

$x^{3} - 23 x^{2} + 142 x - 120 = 0$

$x = 1$ is a root of this equation

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$(x - 1) (x^{2} - 22 x + 120) = 0$

$(x - 1) (x^{2} - 10 x - 120 x + 120) = 0$

$(x - 1) (x (x - 10) - 12 (x - 10)) = 0$

$(x - 1) (x - 12) (x - 10) = 0$

$∴ x = 1, x = 12, x = 10$

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