Form the equation whose roots are
$2, 2, - 2, - 2, 0, 5$ .

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Solution

The equation whose roots are $2, 2, - 2, - 2, 0, 5$ is
$(x - 0) (x - 2) (x + 2) (x - 2) (x + 2) (x - 4) = 0 x (x^{2} - 4) (x^{2} - 4) (x - 5) (x^{2} - 5 x) (x^{4} + 16 - 8 x^{2}) = 0 x^{6} + 16 x^{2} - 8 x^{4} - 5 x^{5} - 80 x + 40 x^{3} = 0 x^{6} - 5 x^{5} - 8 x^{4} + 40 x^{3} + 16 x^{2} - 80 x = 0$

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