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

Algebra ->  Exponential-and-logarithmic-functions -> 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       Log On


   

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) About Me  (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)

   x+=+%28-4+%2B-+sqrt%28+8+%29%29%2F%282%29+=+%28-4+%2B-+sqrt%28+4%2A2+%29%29%2F%282%29++



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