SOLUTION: There are integers $b,c$ for which both roots of the polynomial $x^2-x-1$ are also roots of the polynomial $x^5-bx-c$. Determine the product $bc$.

Question 1075769: There are integers $b,c$ for which both roots of the polynomial $x^2-x-1$ are also roots of the polynomial $x^5-bx-c$. Determine the product $bc$.
Answer by ikleyn(52943) (Show Source): You can put this solution on YOUR website!
.

1.  The roots of the polynomial  are

     =  = .


2.  Substitute the root (the number)  into the polynomial .

    According to the condition, you will get the equation 

     -  -  = 0.


3.  From this point, read my solution to the problem

    https://www.algebra.com/algebra/homework/Expressions-with-variables/Expressions-with-variables.faq.question.1075766.html

    
    https://www.algebra.com/algebra/homework/Expressions-with-variables/Expressions-with-variables.faq.question.1075766.html



4.  Armed with these hints, you are ready / are prepared to complete this assignment on your own.

H a p p y l e a r n i n g !

C o m e a g a i n ! !

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