Form the equation whose roots are
$0, 0, 2, 2, - 3, - 3$ .

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Solution

The equations whose roots are $0, 0, 2, 2, - 3, - 3$ is
$(x - 0) (x - 0) (x - 2) (x - 2) (x + 3) (x + 3) = 0 x^{2} {(x - 2)}^{2} {(x + 3)}^{2} = 0 x^{2} (x^{2} - 4 x + 4) (x^{2} + 6 x + 9) = 0 x^{2} (x^{4} + 6 x^{3} + 9 x^{2} - 4 x^{3} - 24 x^{2} - 36 x + 4 x^{2} + 24 x + 36) = 0 x^{2} (x^{4} + 2 x^{3} - 11 x^{2} - 12 x + 36) = 0 x^{6} + 2 x^{5} - 11 x^{4} - 12 x^{3} + 36 x^{2} = 0$

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