Question

if alpha, beta, gamma are the roots of x^4+2x^2-3x-1 then alpha-^2+beta-^2+gamma-^2 is equal to​

Answer 1

Answer:

As α,β,γ are roots of x

3

+2x

2

+3x+4=0

α+β+γ=−2

αβ+βγ+γα=3

αβγ=−4

Now ∑α

2

β

2

=(α

2

β

2

+β

2

γ

2

+γ

2

α

2

)

=(α+β+γ)

2

−2αβγ(α+β+γ)

=9−2(−2)(−4)=−7

I HOPE THIS IS HELPFUL FOR YOU ☺️