SOLUTION: Given that {{{x^2-5x+4}}} is a factor of {{{x^4+x^3+kx^2+104x-64}}}, evaluate the sum of the four roots of the equation {{{x^4+x^3+kx^2+104x-64=0}}}.

Algebra ->  Equations -> SOLUTION: Given that {{{x^2-5x+4}}} is a factor of {{{x^4+x^3+kx^2+104x-64}}}, evaluate the sum of the four roots of the equation {{{x^4+x^3+kx^2+104x-64=0}}}.      Log On


   

Question 1199518: Given that x%5E2-5x%2B4 is a factor of x%5E4%2Bx%5E3%2Bkx%5E2%2B104x-64, evaluate the sum of the four roots of the equation x%5E4%2Bx%5E3%2Bkx%5E2%2B104x-64=0.
Answer by ikleyn(52802) About Me  (Show Source):
You can put this solution on YOUR website!
.
Given that x%5E2-5x%2B4 is a factor of x%5E4%2Bx%5E3%2Bkx%5E2%2B104x-64, evaluate the sum of the four roots of the equation x%5E4%2Bx%5E3%2Bkx%5E2%2B104x-64=0.
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Due to Vieta's theorem, the sum of the four roots of the equation

    x%5E4%2Bx%5E3%2Bkx%5E2%2B104x-64=0


is equal to the coefficient at  x%5E3  with the opposite sign.


It gives the  ANSWER:  the sum of the four roots of the equation x%5E4%2Bx%5E3%2Bkx%5E2%2B104x-64=0  is -1.

Solved.

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Notice that the answer  DOES  NOT  depend on the premise - - - so that premise can be freely omitted.

It is an  EXCESSIVE  and  NON-NECESSARY  part of the problem.


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My impression is that in your post,  two different problems are mixed in one, by mistake.

Or the problem is presented inadequately.