The number of real solutions of the equation x squared minus 2 times absolute value of x minus 3 equals 0 is:

B. 2 — Let t = |x|, then the equation becomes t^2 - 2t - 3 = 0, which factors to (t-3)(t+1) = 0. Since |x| must be non-negative, we only consider t=3, leading to x = 3 or x = -3.

JEE Main · MathematicsHard

$The number of real solutions of the equation x^{2} - 2∣ x ∣ - 3 = 0 is:$

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

Show correct answer & step-by-step solution

Correct answer: B — $2$

Solution

Let t = ∣ x ∣, then the equation becomes t^{2} - 2 t - 3 = 0, which factors to (t - 3) (t + 1) = 0 . Since ∣ x ∣ \geq 0, we only consider t = 3, leading to x = 3 or x = - 3 .

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The number of real solutions of the equation x2−2∣x∣−3=0 is:

Solution

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More Quadratic Equations practice questions

$The number of real solutions of the equation x^{2} - 2∣ x ∣ - 3 = 0 is:$