Let be four roots of the eqn

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Let α,β,γ,δ\alpha, \beta, \gamma, \delta be four roots of the eqn. x4−4x3+5x2−2x−2=0x^4 - 4x^3 + 5x^2 - 2x - 2 = 0. If the value of 1(α2−2α+3)2+1(β2−2β+3)2+1(γ2−2γ+3)2+1(δ2−2δ+3)2\frac{1}{(\alpha^2 - 2\alpha + 3)^2} + \frac{1}{(\beta^2 - 2\beta + 3)^2} + \frac{1}{(\gamma^2 - 2\gamma + 3)^2} + \frac{1}{(\delta^2 - 2\delta + 3)^2} is ab\frac{a}{b}, (where a,ba, b are coprime numbers), then the value of (a−b)(a-b) is: (A) 4 (B) 7 (C) 1 (D) 9

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