SOLUTION: Find the polynomial with roots alpha, beta and gamma if alpha x beta x gamma = 6, alpha + beta + gamma = 5, and alpha^2 + beta^2 + gamma^2 =21. Help a struggling maths student p

Question 1124748: Find the polynomial with roots alpha, beta and gamma if alpha x beta x gamma = 6, alpha + beta + gamma = 5, and alpha^2 + beta^2 + gamma^2 =21.
Help a struggling maths student please
Answer by ikleyn(52800) (Show Source): You can put this solution on YOUR website!
.

We are given 

     +  +  = 5,            (1)
  
     +  +  = 21.        (2)


It implies

     =  - ( +  + ) =  -  = 4.


Hence,

     = 2.     (3)


Since  ,    and    satisfy  equations 

     +  +  = 5,

     = 2,

    .. = 6,

then by the Vieta's theorem,   ,    and   are the roots of the cubic equation

     = 0.


Answer.  The polynomial with roots  ,    and   satisfying given conditions is   = 0.

Solved.

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