SOLUTION: what is the value of x^4 -6x^3+9x^2-25 if x^2-3x+5=0

Question 1101729: what is the value of x^4 -6x^3+9x^2-25 if x^2-3x+5=0
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
do polynomial division
x^2-3x+5/x^4-6x^3+9x^2+0x-25
==========x^2
=========x^4-3x^3+5x^2 change sign
============-3x^3+4x^2+0x-25
===============-3x
=============-3x^3+9x^2-15x change sign
===================-5x^2+15x-25
======================-5
====================-5x^2+15x-25 change sign
0
the factors are (x^2-3x+5) and (x^2-3x-5)
if x^2-3x+5=0
then x^2-3x=-5
and x^2-3x-5=-10
two of the roots are complex or 3+/-i (sqrt (11) divided by 2
two of the roots are irrational or 3+/-(sqrt(29)/2 which is about -1.12 and 4.19

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