SOLUTION: I need help with another...Please!! Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. Degree 3; zeros: 8, -6-i

Algebra ->  Rational-functions -> SOLUTION: I need help with another...Please!! Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. Degree 3; zeros: 8, -6-i      Log On


   

Question 970035: I need help with another...Please!!
Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f.
Degree 3; zeros: 8, -6-i
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Degree 3;
zeros:
x%5B1%5D=8,
x%5B2%5D=-6-i=>we also have x%5B3%5D=-6%2Bi because complex zeros come always in pairs
then, using zero product rule, f%28x%29 will be:
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29
f%28x%29=%28x-8%29%28x-%28-6-i%29%29%28x-%28-6%2Bi%29%29
f%28x%29=%28x-8%29%28x%2B6%2Bi%29%28x%2B6-i%29
f%28x%29=%28x-8%29%28x%2B6%2Bi%29%28x%2B6-i%29
f%28x%29=%28x-8%29%28x%5E2%2B6x-i%2Ax%2B6x%2B36-6i%2Bxi%2B6i-i%5E2%29
f%28x%29=%28x-8%29%28x%5E2%2B12x%2B36-%28-1%29%29
f%28x%29=%28x-8%29%28x%5E2%2B12x%2B37%29
f%28x%29=x%5E3%2B12x%5E2%2B37x-8x%5E2-96x-296
f%28x%29=x%5E3%2B4x%5E2-59x-296

+graph%28+600%2C+600%2C+-15%2C+15%2C+-355%2C+50%2C+x%5E3%2B4x%5E2-59x-296%29+