The number of roots of the equation |x|^2 - 7 | vedclass

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Question

(D) Given equation: $|x|^2 - 7|x| + 12 = 0$.Let $|x| = t$,where $t \ge 0$.The equation becomes $t^2 - 7t + 12 = 0$.Factoring the quadratic equation: $

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(D) Given equation: $|x|^2 - 7|x| + 12 = 0$.Let $|x| = t$,where $t \ge 0$.The equation becomes $t^2 - 7t + 12 = 0$.Factoring the quadratic equation: $(t - 4)(t - 3) = 0$.This gives two possible values for $t$: $t = 4$ or $t = 3$.Substituting back $|x| = t$:Case $1$: $|x| = 4 \implies x = 4$ or $x = -4$.Case $2$: $|x| = 3 \implies x = 3$ or $x = -3$.Thus,the roots are $x \in \{4, -4, 3, -3\}$.The total number of roots is $4$.

The number of roots of the equation $|x|^2 - 7|x| + 12 = 0$ is

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