(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The roots of the equation [itex]x^3-x-1=0[/itex] are [itex]\alpha,\beta,\gamma[/itex]

[itex]S_n=\alpha^n +\beta^n +\gamma^n[/itex]

(i)Use the relation y=x[itex]^2[/itex] to show that [itex]\alpha^2,\beta^2,\gamma^2[/itex]

are roots of the equation

[itex]y^3-2y^2+y-1=0[/itex]

(ii)Hence, or otherwise find the value of [itex]S_4[/itex]

(iii)Find [itex]S_8,S_{12},S_{16}[/itex]

2. Relevant equations

[tex]\sum \alpha=\frac{-b}{a}

\

\sum \alpha\beta=\frac{c}{a}

\

\sum \alpha\beta\gamma=\frac{-d}{a}[/tex]

3. The attempt at a solution

Just need help with the first part for now. Using I substituted y=x^2 into the equation they gave me in hopes to get back the original equation but that did not work out. Should I just find the sum of the roots and then the sum of the squares of the roots for the original equation and then find the sum of the roots for the eq'n in y and show that they are equal?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Roots of polynomials

**Physics Forums | Science Articles, Homework Help, Discussion**