SOLUTION: Give that the polynomial function has the given zero, find the other zeros. f(x)= {{{x^3-3x^2-5x+39}}} -3 is a zero.

Algebra ->  Functions -> SOLUTION: Give that the polynomial function has the given zero, find the other zeros. f(x)= {{{x^3-3x^2-5x+39}}} -3 is a zero.      Log On


   

Question 240964: Give that the polynomial function has the given zero, find the other zeros.
f(x)= x%5E3-3x%5E2-5x%2B39 -3 is a zero.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=x%5E3-3x%5E2-5x%2B39


-3 | 1 -3 -5  39
   |   -3 18 -39
    ------------
     1 -6 13   0

So now you have factored the 
polynomial f(x) this far:

f%28x%29=%28x%2B3%29%28x%5E2-6x%2B13%29

The zeros are found by setting
this equal to 0:

%28x%2B3%29%28x%5E2-6x%2B13%29=0

x%2B3=0 give the zero -3 which was given.

x%5E2-6x%2B13=0 will give the other zeros.

But this will not factor so we must use the
quadratic formula:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ 

with a=1, b=-6, and c=13

x+=+%28-%28-6%29+%2B-+sqrt%28%28-6%29%5E2-4%2A%281%29%2A%2813%29+%29%29%2F%282%2A%281%29%29+

x+=+%286+%2B-+sqrt%2836-52+%29%29%2F2+

x+=+%286+%2B-+sqrt%28-16%29%29%2F2+

x+=+%286+%2B-+i%2Asqrt%2816%29%29%2F2+

x+=+%286+%2B-+i%2A4%29%2F2+

x+=+%286+%2B-+4i%29%2F2+

x+=+6%2F2+%2B-+4i%2F2+


x+=+3+%2B-+2i+ 

The other zeros are 3%2B2i and 3-2i

Edwin