BITSAT 2012 Paper

We have, x = ω – ω2 –2 or x + 2 = ω – ω2
Squaring, x2 + 4x + 4 = ω2+ω4–2ω3
= ω2+ω3ω.–2ω3 = ω2+ω – 2 [ω3 = 1]
= –1 – 2 = – 3 ⇒ 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