(C) Given the equation: $x^2-5|x|-14=0$.Since $x^2 = |x|^2$,we can rewrite the equation as:$|x|^2-5|x|-14=0$.Let $t = |x|$,where $t \geq 0$. The equat

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(C) Given the equation: $x^2-5|x|-14=0$.Since $x^2 = |x|^2$,we can rewrite the equation as:$|x|^2-5|x|-14=0$.Let $t = |x|$,where $t \geq 0$. The equation becomes $t^2-5t-14=0$.Factoring the quadratic: $(t-7)(t+2)=0$.This gives $t=7$ or $t=-2$.Since $t = |x| \geq 0$,we reject $t=-2$.Thus,$|x|=7$,which implies $x=7$ or $x=-7$.Both roots are real. Therefore,there are exactly two real roots.

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

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For the equation $x^2-5|x|-14=0$,which of the following is true?

AP EAMCET 2021 All AP EAMCET

A
all roots are real
B
all the roots are imaginary
C
two roots are real
D
no real roots

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4-2.Quadratic Equations and Inequations

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Solution of quadratic equations and Nature of roots

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For the equation $x^2-5|x|-14=0$,which of the following is true?

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