SOLUTION: find all the REAL zeros of the function x^4-4x^3+4x-1

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Question 427393: find all the REAL zeros of the function x^4-4x^3+4x-1
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Solution:First we factor the function:
%28x%5E4-1%29-4x%28x%5E2-1%29=
%28x%5E2-1%29%2A%28x%5E2%2B1%29-4x%28x%5E2-1%29=
%28x%5E2-1%29%2A%28x%5E2%2B1-4x%29=
%28x-1%29%28x%2B1%29%28x%5E2-4x%2B1%29 To find all the zeros equalize to zero all the factors:
x-1=0 => x=1; x+1=0 => x=-1;
x%5E2-4x%2B1=0 =>
x=2%2B-+sqrt%283%29
The solution set of this function is:{-1, 1, 2+-sqrt(3)}
graph%28400%2C+400%2C+-5%2C+5%2C+-16%2C+5%2C+x%5E4-4x%5E3%2B4x-1%29