Multiple choice

If α, β, γ are roots of the equation x3 - 3x2 + 3x + 7 = 0 (and ω is imaginary cube root of unity), then find the value of (α - 1)/(β - 1) + (β - 1)/(γ - 1) + (γ - 1)/(α - 1).

  1. ω2

  2. ∞ (infinity)

  3. 3

  4. 3ω2

  5. 0
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

x3-3x2+3x+7=0 (x-1)3+8=0 (x-1)3=-8 (x-1)3=(-2)3 {(x-1)/(-2)}3=(1) Taking the cube root, we get (x-1)/(-2)=1,ω,ω2 Solving, we get three different values of x or α, β, γ = -1, 1-2ω, 1-2ω2 Putting the values of α, β, γ in the asked equation, (1/ω)+(1/ω)+ω2=3ω2 (As 1 can be written as ω3)(Correct Answer)

Keep practicing — related questions