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}}}.

Question 1199518: Given that is a factor of , evaluate the sum of the four roots of the equation .
Answer by ikleyn(52802) (Show Source): You can put this solution on YOUR website!
.
Given that is a factor of , evaluate the sum of the four roots of the equation .
~~~~~~~~~~~~~~~~~~

Due to Vieta's theorem, the sum of the four roots of the equation

    


is equal to the coefficient at    with the opposite sign.


It gives the  ANSWER:  the sum of the four roots of the equation   is -1.

Solved.

-----------------

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.

////////////////

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

Or the problem is presented inadequately.

RELATED QUESTIONS
Given that x^2+5x-14 is a factor of x^4-2x^3-37x^2+kx-168, evaluate the sum of the four... (answered by ikleyn)

Given that x^2+5x-14 is a factor of x^4-2x^3-37x^2+kx-168, evaluate the sum of the four... (answered by ikleyn)

Given that {{{ x^2-3x+2 }}} is a factor of {{{ x^4+kx^3-10x^2-20x+24 }}}, evaluate the... (answered by Boreal,ikleyn)

Given that {{{ x^2-3x+2 }}} is a factor of {{{ x^4 + kx^3 - 10x^2 - 20x+24 }}} evaluate... (answered by ikleyn,MathTherapy)

Find the value of k such that x-2 is a factor of kx^3 - kx^2 + x+2 (answered by ikleyn)

Find the 4 roots of the equation: x^4+kx^2+1=0... (answered by Nate)

Determine the value of k in f(x) = 5x^3+kx^2-4x+4 so that x+2 is a factor (answered by MathLover1)

find k such that f(x) = x^4 - kx^3 + kx^2 + 1 has the factor... (answered by jsmallt9)

if x+1 is a factor of x^3+3x^2+kx+4, find the value of... (answered by Boreal,ikleyn)