The product and sum of the roots of the equat | vedclass

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Question

(A) Given equation: $|x|^2 - 5|x| - 24 = 0$. Let $|x| = t$,where $t \ge 0$. The equation becomes $t^2 - 5t - 24 = 0$. Factoring the quadratic: $(t - 8

Vedclass · Accepted Answer

$-64, 0$

Vedclass · Answer

(A) Given equation: $|x|^2 - 5|x| - 24 = 0$. Let $|x| = t$,where $t \ge 0$. The equation becomes $t^2 - 5t - 24 = 0$. Factoring the quadratic: $(t - 8)(t + 3) = 0$. This gives $t = 8$ or $t = -3$. Since $|x| \ge 0$,we reject $t = -3$. Thus,$|x| = 8$,which implies $x = 8$ or $x = -8$. The roots of the equation are $8$ and $-8$. Product of the roots: $8 	imes (-8) = -64$. Sum of the roots: $8 + (-8) = 0$. Therefore,the product and sum are $-64$ and $0$ respectively.

The product and sum of the roots of the equation $|x|^2 - 5|x| - 24 = 0$ are respectively:

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