SOLUTION: Find the irrational roots of the equation x^3-4x^2+2x+1=0

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Question 38939: Find the irrational roots of the equation x^3-4x^2+2x+1=0
Found 2 solutions by stanbon, fractalier:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the irrational roots of the equation x^3-4x^2+2x+1=0
The coefficients add up to zero so "1" is a root and "x-1"
is a factor.
Divide by x-1 to get x^2-3x-1
Use the quadratic formula to find the irrational zeroes:
x=[3+sqrt(9+4)]/2 or x=[3-sqrt(9+4)]/2

Cheers,
Stan H.

Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
If we can see that 1 is a root of
x^3 - 4x^2 + 2x + 1 = 0
we can factor out x - 1 and get
(x - 1)(x^2 - 3x - 1) = 0
Using the quadratic formula on the second polynomial, we get
x = (3 ± sqrt(13)) / 2 in addition to x = 1