Find the root of the equation $x^{3} - 6 x^{2} + 11 x - 6 = 0$

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Solution

$x^{3} - 6 x + 11 x - 6 = 0$
Put $X = 1$
$1 - 6 + 11 - 6 = 0$
$1$ is root of equation, so $(x - 1)$ is factor of $x^{3} - 6 x^{2} + 11 x - 6$
$x^{2} - 5 x + 6 = 0$
$(x - 3) (x - 2) = 0$
$x = 2, 3$
root of cubic equation $= 1, 2, 3$

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