(D) Given the 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

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(D) Given the 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 $t = 4$ or $t = 3$.Substituting back $|x| = t$:Case $1$: $|x| = 4 \implies x = 4, -4$.Case $2$: $|x| = 3 \implies x = 3, -3$.Thus,the roots are $4, -4, 3, -3$.The total number of roots is $4$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic equations and Nature of roots

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

A
$1$
B
$2$
C
$3$
D
$4$

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4-2.Quadratic Equations and Inequations

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

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