SOLUTION: Form a​ fifth-degree polynomial function with real coefficients such that i, 1-2i, and -4 are zeros and f(0)=40

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Form a​ fifth-degree polynomial function with real coefficients such that i, 1-2i, and -4 are zeros and f(0)=40      Log On


   

Question 1041825: Form a​ fifth-degree polynomial function with real coefficients such that i, 1-2i, and -4 are zeros and f(0)=40
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Real coefficients means complex roots come in complex conjugate pairs.
f%28x%29=a%28x-i%29%28x%2Bi%29%28x-%281-2i%29%29%28x-%281%2B2i%29%29%28x%2B4%29
f%28x%29=a%28x%5E2%2B1%29%28x%5E2-2x%2B5%29%28x%2B4%29
So when,
x=0,
f%280%29=a%281%29%285%29%284%29
40=a%2820%29
a=2
So,
f%28x%29=2%28x%5E2%2B1%29%28x%5E2-2x%2B5%29%28x%2B4%29
highlight%28f%28x%29=2x%5E5%2B4x%5E4-4x%5E3%2B44x%5E2-6x%2B40%29