SOLUTION: If the solution for x of x^2+px+q=0 are the cubes of the solutions for x^2+mx+n=0, express p and q in terms of m and n.

Question 1121162: If the solution for x of x^2+px+q=0 are the cubes of the solutions for x^2+mx+n=0, express p and q in terms of m and n.
Answer by ikleyn(52777) (Show Source): You can put this solution on YOUR website!
.

Let    and    be the roots to the second equation.


Then, according to Vieta's theorem,


     +  = - m;   . = n.      (1)



According to the condition, the roots of the first equation are    and  .


Then, according to the Vieta's theorem


    p =  =  =  = ,


    q =  =  = .


Answer.  Under the given conditions,  p =   and  q = .

Solved.

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