Question

The number of real roots of the equation $x^2+5\mid x\mid +4=0$ is $\underset{–}{}$

Answer 1

We have,

$x^2+5\mid x\mid +4=0$

$\Rightarrow \mid x{\mid }^2+5\mid x\mid +4=0$

$\Rightarrow \mid x{\mid }^2+\mid x\mid +4\mid x\mid +4=0$

$\Rightarrow \mid x\mid (\mid x\mid +1)+4(\mid x\mid +1)=0$

$\Rightarrow (\mid x\mid +1)(\mid x\mid +4)=0$

$\Rightarrow \mid x\mid +1=0$ or $\mid x\mid +4=0$

$\Rightarrow \mid x\mid =-1$ or $\mid x\mid =-4$

Which is not possible.

Hence, the number of real roots is $0$.

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