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Nature of Roots

The number of...

Question

The number of real roots of the equation $x^{2} + 5 ∣ x ∣ + 4 = 0$ is $- ---- -$

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Solution

We have,

$x^{2} + 5 ∣ x ∣ + 4 = 0$

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

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

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

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

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

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

Which is not possible.

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

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Nature of Roots

Standard XIII Mathematics

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