Question

Sum of roots of equation : (x + 3)² – 4 |x + 3| + 3 = 0 is :

• A. 4
• B. 12
• C. – 12
• D. – 4

Answer 1

Answer: (C)

– 12

Answer 2

(x+3)²–4 (x+3)+3 = 0 or (x+3)² + 4 (x+3) + 3 = 0

(x ≥ – 3) (x < – 3)

⇒ x² + 2x = 0 ⇒ x² + 10 x + 24 = 0

x = 0, – 2 (both possible)

⇒ x=–4, – 6 (both possible)

so, sum of roots = 0 – 2 – 4 – 6 = – 12