help with a polynomial question (1 Viewer)

[Naylyn]

can someone please help me with this question, it is from an ancient Patel text book. This is question 3 part b.

x^4+x^3+2x^2+3x+4=0

evaluate: (alpha^2)*beta + (beta^2)*gamma + (gamma^2)*alpha+alpha*beta^2+beta*gamma^2+gamma*alpha^2

The hint is; use (alpha+beta+gamma)(alpha*beta+beta*gamma+gamma*alpha) and expand.

 

[vafa]

how come you have 3 roots and not 4 roots...
your polynomial is of degree 4

 

[vafa]

the question may be wrong because you have a polynomial of degree 4 and you have only 3 roots(alpha,beta,gamma)

but if this is is a third degree polynomial, you should have no problem with that.

 

[Naylyn]

the question may be wrong because you have a polynomial of degree 4 and you have only 3 roots(alpha,beta,gamma)

but if this is is a third degree polynomial, you should have no problem with that.

It is definately a polynomial of degree 4, and part a) of the question asked you to find alpha^2 + gamma^2 + beta^2 + delta^2. I thought the question might be a misprint but i decided to post the question here just in case it can be done.

 

[buchanan]

The 2nd edition of Patel's Foundations of 4 Unit Mathematics has as Exercise 5D, question 3b:

If α, β, γ, δ are the roots of x⁴+x³+2x²+3x+4=0, evaluate αβ+αγ+αδ+βγ+βδ+γδ

And the answer is 2 (sum of roots 2 at a time).

 

[vafa]

so from my understandin there should be a delta as well and the question is wrong in the old version.

i know that a polynomial of degree 4 can be changed to a polynomial of degree 2 if we have ax^4+bx^3+cx^2+-bx+a=0 but i never have tried to make it a third degree polynomial.

 

[buchanan]

there should be a delta as well and the question is wrong in the old version.

Yep.