SOLUTION: Find all the roots or zeros for the following polynomial. f(x)=x^4-2x^3+5x^2-8x+4

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find all the roots or zeros for the following polynomial. f(x)=x^4-2x^3+5x^2-8x+4       Log On


   

Question 1061009: Find all the roots or zeros for the following polynomial.
f(x)=x^4-2x^3+5x^2-8x+4

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
x^4-2x^3+5x^2-8x+4
===1===-2===5====-8====4
----1===-1===4====-4-----0
1 is the root, (x-1) the factor.
Notice that f(1)=1-2+5-8+4=0
The next polynomial is
x^3-x^2+4x-4
====1===-1===4====-4
try 1
-----1====0===4=====0
(x-1) is a factor with multiplicity 2 (graphical "bounce") ANSWER
left with x^2+4, which has roots of +/- 2i ANSWER
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E4-2x%5E3%2B5x%5E2-8x%2B4%29