SOLUTION: Find the complex zeros of the polynomial function. Write f in factored form f(x)=x^3+343

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find the complex zeros of the polynomial function. Write f in factored form f(x)=x^3+343      Log On


   

Question 668772: Find the complex zeros of the polynomial function. Write f in factored form
f(x)=x^3+343
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = x^3 + 343 = x^3 + 7^3 <--- important to recognize this since for (a^3 + b^3) = (a+b)(a^2-ab+b^2) where a=x and b = 7
(x+7)(x^2-7x+49)
highlight%28x+=+-7%29
(x^2-7x+49) use quadratic formula
x+=+%287+%2B-+sqrt%2849-4%2A49%2A1%29%29%2F%282%29
x+=+%287+%2B-+sqrt%2849-196%29%29%2F2
x+=+%287+%2B-+sqrt%28-147%29%29%2F2
x+=+%287+%2B-+i%2Asqrt%283%2A49%29%29%2F2
x+=+highlight%28%287+%2B-+7i%2Asqrt%283%29%29%2F2%29