SOLUTION: For the polynomial below, -2 is a zero. h(x)=x^3+8x^2+14x+4 Find the other zeros.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: For the polynomial below, -2 is a zero. h(x)=x^3+8x^2+14x+4 Find the other zeros.      Log On


   

Question 1099422: For the polynomial below, -2 is a zero. h(x)=x^3+8x^2+14x+4
Find the other zeros.
Found 2 solutions by josgarithmetic, Edwin McCravy:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
h(x) divided by (x+2) gives a quadratic polynomial and you can then find those zeros. (Two irrational zeros)

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
h(x)=x³+8x²+14x+4

Since -2 is a zero we can form this synthetic division
and get 0 remainder

-2|1  8  14  4
  |  -2 -12 -4
   1  6   2  0

And that means that h(x) factors this way

h(x) = (x+2)(x²+6x+2)

       x+2 = 0;      x²+6x+2 = 0
         x = -2;           x+=+%28-6+%2B-+sqrt%286%5E2-4%281%292%29%29%29%2F%282%2A1%29 
                           x+=+%28-6+%2B-+sqrt%2836-8%29%29%29%2F2
                           x+=+%28-6+%2B-+sqrt%2828%29%29%29%2F2   
                           x+=+%28-6+%2B-+sqrt%284%2A7%29%29%29%2F2
                           x+=+%28-6+%2B-+2sqrt%287%29%29%29%2F2
                           x+=+%28-6%29%2F2+%2B-+2sqrt%282%29%2F2
                           x+=+-3+%2B-+sqrt%287%29  

The other zeros are -3%2Bsqrt%287%29 and  -3-sqrt%287%29. 
          
Edwin