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Black Advanced Problems in Mathematics
Exam
Black Advanced Problems in Mathematics
Subject
Mathematics
Chapter
Quadratic Equation

Black Advanced Problems in Mathematics · Mathematics · Quadratic Equation

Let α, β, γ, are roots of x^4 - 12x^3 + λ x^2 - 54x + 14 = 0 . If α...

Let α,β,γ,δ\alpha, \beta, \gamma, \delta are roots of x4−12x3+λx2−54x+14=0x^4 - 12x^3 + \lambda x^2 - 54x + 14 = 0. If α+β=γ+δ\alpha + \beta = \gamma + \delta, then

Options

  1. Aλ=45\lambda = 45
  2. Bλ=−45\lambda = -45
  3. CIf α2+β2<γ2+δ2\alpha^2 + \beta^2 < \gamma^2 + \delta^2 then αβγδ=72\frac{\alpha\beta}{\gamma\delta} = \frac{7}{2}
  4. DIf α2+β2<γ2+δ2\alpha^2 + \beta^2 < \gamma^2 + \delta^2 then αβγδ=27\frac{\alpha\beta}{\gamma\delta} = \frac{2}{7}.

Correct answer

A. λ=45\lambda = 45

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