Relation Between Roots and Coefficients for Higher Order Equations
If α, β, γ, δ...
Question
If α,β,γ,δ∈R satisfy (α+1)2+(β+1)2+(γ+1)2+(δ+1)2α+β+γ+δ=4.
If the equation a0x4+a1x3+a2x2+a3x+a4=0 has the roots (α+1β−1),(β+1γ−1),(γ+1δ−1),(δ+1α−1), then the value of a2a0 is
A
6.00
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B
6.0
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C
6
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Solution
(α−1)2+(β−1)2+(γ−1)2+(δ−1)2=0 α=β=γ=δ=1
So, all the roots are (1+1-1)=1
So, the equation is (x−1)4=0 x4−4x3+6x2−4x+1=0 a2a0=61=6