Question 81

The number of real solutions of the equation $$x|x + 5| + 2|x + 7| - 2 = 0$$ is _________

Name: The number of real solutions of the equation x|x + 5| + 2|x + 7| - 2 = 0 is _________
Uploaded: 2026-05-30T17:02:24.876714+05:30
Duration: 7 min 38 s
Description: The number of real solutions of the equation x|x + 5| + 2|x + 7| - 2 = 0 is _________

Correct Answer: 3

Solution

$$x \geq -5$$: $$x^2+7x+12=0 \implies x = -3, -4$$ (2 solutions).

$$-7 \leq x < -5$$: $$-x^2-3x+12=0 \implies x = \frac{-3-\sqrt{57}}{2} \approx -5.27$$ (1 solution).

$$x < -7$$: $$-x^2-7x-16=0 \implies D < 0$$ (0 solutions).

Total: 3

Get AI Help

Video Solution

Create a FREE account and get:

Free JEE Mains Previous Papers PDF
Take JEE Mains paper tests

The number of real solutions of the equation $$x|x + 5| + 2|x + 7| - 2 = 0$$ is _________

Solution

Get AI Help

Video Solution

Download resources