SOLUTION: Find a third degree polynomial function f(x) with real coefficients that has -2, 3i, and -3i as zeros and such that f(-1)= 20

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find a third degree polynomial function f(x) with real coefficients that has -2, 3i, and -3i as zeros and such that f(-1)= 20      Log On


   

Question 437165: Find a third degree polynomial function f(x) with real coefficients that has -2, 3i, and -3i as zeros and such that f(-1)= 20
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The constant term: -(-2)(3i)(-3i) = 18
The coefficient of x: (-2)(3i) + (-2)(-3i) + (3i)(-3i) = 9
The coefficient of x%5E2: -(-2 + 3i - 3i) = 2.
The coefficient of x%5E3: 1
Hence the polynomial is f%28x%29+=+c%28x%5E3+%2B+3x%5E2+%2B+9x+%2B+18%29
Now 20+=+c%28%28-1%29%5E3+%2B+3%2A%28-1%29%5E2+%2B++9%28-1%29+%2B+18%29+=+10c
==> c = 2.
The polynomial is f%28x%29+=+2%28x%5E3+%2B+3x%5E2+%2B+9x+%2B+18%29.