SOLUTION: Find the complex zeros of the following polynomial function. Write f in factored form. f(x)= x^3-1

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find the complex zeros of the following polynomial function. Write f in factored form. f(x)= x^3-1       Log On


   

Question 1151674: Find the complex zeros of the following polynomial function. Write f in factored form.
f(x)= x^3-1
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=+x%5E3-1+
f%28x%29=+%28x+-+1%29+%28x%5E2+%2B+x+%2B+1%29...set f%28x%29=0
+%28x+-+1%29+%28x%5E2+%2B+x+%2B+1%29=0=> real zero is x=1

if %28x%5E2+%2B+x+%2B+1%29=0.......use quadratic formula

x+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A1+%29%29%2F%282%2A1%29+
x+=+%28-1+%2B-+sqrt%28+1-4%29%29%2F2+
x+=+%28-1+%2B-+sqrt%28+-3%29%29%2F2+

x+=+%28-1+%2B-+%28sqrt%28-1%29%2Asqrt%28+3%29%29%29%2F2+

x+=+%28-1+%2B-+i%2Asqrt%28+3%29%29%2F2+



complex solutions:
x+=+%28-1+%2B+i%2Asqrt%28+3%29%29%2F2+ =>x+=+-1%2F2+%2B+i%2Asqrt%28+3%29%2F2+
x+=+%28-1+-+i%2Asqrt%28+3%29%29%2F2+ =>x+=+-1%2F2+-+i%2Asqrt%28+3%29%2F2+