If α, β, γ are the roots of x3-2 x2+3 x-4=0 then the value of α2 β2+β2 γ2+γ2 α2 is

Question

If α, β, &gamma; are the roots of x3-2 x2+3 x-4=0 then the value of α2 β2+β2 &gamma;2+&gamma;2 α2 is (A) -7 (B) -5 (C) -3 (D) 0

Tardigrade Admin · Accepted Answer

If α, β, &gamma; are the roots of the equation x3-2 x2+3 x-4=0, then α+β+&gamma;=(2/1)=2 α β+β &gamma;+&gamma; α=3 and α β &gamma;=4 We know that α2 β2+ β2 &gamma;2+&gamma;2 α2 =(α β+β &gamma;+&gamma; α)2-2(α β &gamma;)(α+β+&gamma;) =(3)2-2(4)(2) =9-16 =-7

Q. If α,β,γ are the roots of x3−2x2+3x−4=0 then the value of α2β2+β2γ2+γ2α2 is

-7

-5

-3

0

If α,β,γ are the roots of the equation x3−2x2+3x−4=0, then α+β+γ=12​=2 αβ+βγ+γα=3 and αβγ=4 We know that α2β2+β2γ2+γ2α2 =(αβ+βγ+γα)2−2(αβγ)(α+β+γ) =(3)2−2(4)(2) =9−16 =−7

Q. If $α, β, γ$ are the roots of $x^{3} - 2 x^{2} + 3 x - 4 = 0$ then the value of $α^{2} β^{2} + β^{2} γ^{2} + γ^{2} α^{2}$ is