Question

If α ,β ,γ,δ are roots of x4+ 4x3– 6x2+ 7x – 9 = 0, then the value of (1 + α2)(1 + β2)(1 + γ2)(1 + δ2) is

(a) 9

(b) 11

(c) 13

(d) 5

Answer 1

Correct option (c) 13

Explanation:

x4+ 4x3– 6x2+ 7x – 9 = (x - α)(x - β)(x - γ)(x - δ)

Put x = i, i4+ 4i3– 6i2+ 7i – 9 = (i- α)(i - β)(i - γ)(i - δ)

–2 + 3i = (i- α)(i - β)(i - γ)(i - δ) ...(1)

Put x = – i

– 2 – 3i = (-i- α)(-i - β)(-i - γ)(-i - δ) ....(2)

Multiply (1) & (2)

4–9i2 = (α2 + i2)(β2 + i2)(γ2 - i2)(δ2 - i2)

13 = (1 + α2)(1+ β2)(1 + γ2)(1 + δ2)