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प्रश्न
Find the sum of squares of roots of the equation `2x^4 - 8x^3 + 6x^2 - 3` = 0
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उत्तर
The given equation is 2x4 – 8x3 + 6x2 – 3 = 0.
(÷ 2) ⇒ `x^4 - 4x^3 + 3x^2 - 3/2` = 0
Let the roots be α, β, γ, δ
α + β + γ + δ = – b = 4
(αβ + βγ + γδ + αδ + αγ + βδ) = c = 3
αβγ + βγδ + γδα = – d = 0
αβγδ = `(-3)/2`
To Find α2 + β2 + γ2 + δ2 = (α + β + γ + δ)2 – 2(αβ +
βγ + γδ + αδ + αγ + βδ)
= (4)2 – 2(3)
= 16 – 6
= 10
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