Number of solutions of the equations $| 2 x^{2} + x - 1 | = | x^{2} + 4 x + 1 |$ .

1

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2

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3

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4

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Solution

The correct option is D $4$
$∣ ∣ 2 x^{2} + x - 1 ∣ ∣ = ∣ ∣ x^{2} + 4 x + 1 ∣ ∣$
$2 x^{2} + x - 1 = - (x^{2} - 4 x + 1)$
$3 x^{2} - 5 x = 0$
$x (3 x - 5) = 0$
$x = 0 o r \frac{5}{3}$
or
$2 x^{2} + x - 1 = x^{2} + 4 x + 1$
$x^{2} - 3 x - 2 = 0$
$x = \frac{3 \pm \sqrt{9 + 8}}{2}$
$x = \frac{3 + \sqrt{17}}{2}, \frac{3 - \sqrt{17}}{2}$
$∴$ answer is $4$

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