For the equation |x^2| + |x| - 6 = 0,the root | vedclass

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(C) Given equation: $|x^2| + |x| - 6 = 0$.Since $|x^2| = |x|^2$,the equation can be written as $|x|^2 + |x| - 6 = 0$.Let $t = |x|$,where $t \ge 0$. Th

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(C) Given equation: $|x^2| + |x| - 6 = 0$.Since $|x^2| = |x|^2$,the equation can be written as $|x|^2 + |x| - 6 = 0$.Let $t = |x|$,where $t \ge 0$. The equation becomes $t^2 + t - 6 = 0$.Factoring the quadratic: $(t + 3)(t - 2) = 0$.This gives $t = -3$ or $t = 2$.Since $t = |x| \ge 0$,we discard $t = -3$.Thus,$|x| = 2$,which implies $x = 2$ or $x = -2$.The roots are $2$ and $-2$.The sum of the roots is $2 + (-2) = 0$.

For the equation $|x^2| + |x| - 6 = 0$,the roots are

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