Obtains all other zeroes of $x^{4} - 3 x^{3} - x^{2} + 9 x - 6$ , if two of its zeroes are $\sqrt{3}$ and $- \sqrt{3}$

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Solution

$x^{4} - 3 x^{3} - x^{2} + 9 x - 6 = 0$
$(x + \sqrt{3}) (x - \sqrt{3}) = x^{3} - 3$
Refer above image for factorization
$⟹ (x^{2} - 3) (x^{2} - 3 x + 2) = 0$
$⟹ (x^{2} - 3) (x^{2} - 2 x - x + 2) = 0$
$⟹ x = 2, 1, \sqrt{3}, - \sqrt{3}$

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