Question

If x = w – w² – 2, then the value of x⁴ + 3x³ + 2x² – 11x – 6 is

• A. 1
• B. –1
• C. 2
• D. None of these

Answer 1

Answer: (A)

1

Answer 2

Sol. We have, x = w – w² – 2 or x + 2 = w – w²

Squaring, x² + 4x + 4 = w² + w⁴ – 2w³

= w² + w³ . w – 2w³

= w² + w – 2 [Q w³ = 1]

= –1 – 2 = –3,

Ž x² + 4x + 7 = 0.

Dividing x⁴ + 3x³ + 2x² – 11x – 6 by x² + 4x + 7, we get,

x⁴ + 3x³ + 2x² – 11x – 6 = (x² + 4x + 7) (x² – x – 1) + 1

= (0) (x² – x – 1) + 1

= 0 + 1 = 1.