SOLUTION: Find the complex zeros of the polynomial. Write f in factored form. f(x)=x^3-512

Algebra ->  Inequalities -> SOLUTION: Find the complex zeros of the polynomial. Write f in factored form. f(x)=x^3-512      Log On


   

Question 636743: Find the complex zeros of the polynomial. Write f in factored form. f(x)=x^3-512
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

Find the complex zeros of the polynomial.

f(x)=x^3-512   |Note x = 8, a real root

using synthetic Division:

8	1	0	  0	-512

 	 	8	 64	 512

 	1	8	 64	   0

yields

      x^2 + 8x + 64 = 0

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

 x+=+%28-8+%2B-+sqrt%28+-192%29%29%2F%282%29+

 x+=+%28-8+%2B-+sqrt%28%28-1%29%2A64%2A3%29%29%2F%282%29+

      +x+=+-4+%2B-+4i%2Asqrt%283%29