SOLUTION: Hi, im really having trouble with this one question since i have missed the class this was taught. i would really appreciate the help! Question: Find a FOURTH DEGREE polynomial

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi, im really having trouble with this one question since i have missed the class this was taught. i would really appreciate the help! Question: Find a FOURTH DEGREE polynomial       Log On


   

Question 1054384: Hi, im really having trouble with this one question since i have missed the class this was taught. i would really appreciate the help!
Question: Find a FOURTH DEGREE polynomial f(x) with real coefficients that has roots of : -2, 1, and 3i with f(3)= -12

Thank you!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Polynomials with real solutions, if they have a complex root, they also have the complex conjugate as a root.
So since x=3i is a root, x=-3i is also a root.
So forming the solution polynomial,
f%28x%29=a%28x%2B2%29%28x-1%29%28x-3i%29%28x%2B3i%29
f%28x%29=a%28x%5E2%2Bx-2%29%28x%5E2%2B9%29
f%28x%29=a%28x%5E4%2Bx%5E3%2B7x%5E2%2B9x-18%29
Solve for a using the given value.
f%283%29=a%283%5E4%2B3%5E3%2B7%283%29%5E2%2B9%283%29-18%29=-12
f%283%29=a%28180%29=-12
a=-12%2F180
a=-1%2F15
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f%28x%29=%28-1%2F15%29%28x%5E4%2Bx%5E3%2B7x%5E2%2B9x-18%29
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