Question

The sum of real roots of the equation x² + |x| - 6 = 0 is
1. 4
2. 5
3. 0
4. -1

Answer 1

Correct Answer - Option 3 : 0

Calculation:

x2 + |x| - 6 = 0

Case 1: When x > 0, then |x| = x

⇒ x² + x - 6 = 0

⇒ x² + 3x - 2x - 6 = 0

⇒ x(x + 3) - 2(x + 3) = 0

⇒ (x + 3)(x - 2) = 0

⇒ x = -3, 2

Case 2: When x < 0, then |x| = -x

⇒ x2 - x - 6 = 0

⇒ x2 - 3x + 2x - 6 = 0

⇒ x(x - 3) + 2(x - 3) = 0

⇒ (x - 3)(x + 2) = 0

⇒ x = 3, -2

Thus, the sum of real roots = -3 + 2 + 3 - 2 = 0

Hence, The sum of real roots of the equation x2 + |x| - 6 = 0 is 0.