SOLUTION: Find a rational zero of the polynomial function and use it to find all the zeros of the function. f(x) = x3 + 5x2 + 6x + 2

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Question 468363: Find a rational zero of the polynomial function and use it to find all the zeros of the function.
f(x) = x3 + 5x2 + 6x + 2

Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
 
Hi,
f(x) = x3 + 5x2 + 6x + 2 | x = -1 a root as -1 + 5 - 6 + 2 = 0
Using synthetic division
(x3 + 5x2 + 6x + 2)/(x+1) = x^2 + 4x + 2
-1 1 5 6 2
-1 -4 -2
1 4 2 0
(x+1)(x^2 + 4x + 2)

zeros are: -1, -2+sqrt(2),-2-sqrt(2)
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