(C) Given the equation $x^{2}-|x|-12=0$.Since $x^{2} = |x|^{2}$,we can rewrite the equation as $|x|^{2}-|x|-12=0$.Let $t = |x|$,where $t \geq 0$. The

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(C) Given the equation $x^{2}-|x|-12=0$.Since $x^{2} = |x|^{2}$,we can rewrite the equation as $|x|^{2}-|x|-12=0$.Let $t = |x|$,where $t \geq 0$. The equation becomes $t^{2}-t-12=0$.Factoring the quadratic equation: $(t-4)(t+3)=0$.This gives $t=4$ or $t=-3$.Since $t = |x| \geq 0$,we reject $t=-3$.Thus,$|x|=4$,which implies $x=4$ or $x=-4$.Therefore,there are $2$ real solutions.

Class 11 Mathematics 2 Complex Numbers and Quadratic Equations: Quadratic Equations Solution of quadratic equations and Nature of roots

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The number of real solutions of the equation $x^{2}-|x|-12=0$ is:

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

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2 Complex Numbers and Quadratic Equations: Quadratic Equations

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If a polynomial $x^4+x^2+1$ is divisible by $x^2+mx+1$ and $x^2+nx+1$,then $m+n$ is equal to:
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