Question

If a,ß, y be zeros of (x³+ x+17) then polynomial whose zeros are alpha – 2, beta– 2, gama- 2 is looks like K((x +A)³ +(x +B) + C) then (A+ B+C) IS​

Answer 1

Step-by-step explanation:

Solution :

a)α+β+γ=0

αβ+βγ+γα=q

αβγ=−r

2(α+β+γ)=0=b

x3−bx2+cx−d=0

C=αβ+αγ+β2+βγ+βα+γ2+γα+αβ+α2+αβ

c=(α+β+γ)2+(αβ+γβ+αγ)

c=q

d=(α+β)(β+γ)(γ+α)

d=αβ+αγ+β2+βγ)(α+γ)

d=αβγ+αγ2+β2γ+βγ2+α2β+α2γ+β2γ+αβγ

d=r

x3+2x+r=0

b)b=αβ+βγ+γα=q

c=αβ2γ+βγa2α+α2βγ

=αβγ(α+β+γ)=0

d=α2β2γ2=r2

x3−qx2+0x−r2=0

x3−qx2−r2=0.