SOLUTION: find the polynomial function with the given zeros -5,2-i,2+1

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Question 665647: find the polynomial function with the given zeros -5,2-i,2+1
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

2%2B1 this is probably 2%2Bi
the given zeros x%5B1%5D=-5,x%5B2%5D=2-i,x%5B3%5D=2%2Bi...you have three zeros, so your polynomial is third degree polynomial; so, we have

%28x+-+x%5B1%5D%29%28x+-+x%5B2%5D%29%28x+-+x%5B3%5D%29

%28x+-+%28-5%29%29%28x+-+%282-i%29%29%28x+-+%282-i%29%29

%28x+%2B5%29%28x+-2%2Bi%29%28x+-2%2Bi%29

%28x%5E2-2x%2Bxi%2B5x-10%2B5i%29%28x+-2%2Bi%29




x%5E3%2Bx%5E2-20x-x%2B4x%2B%28x%5E2%2B5x-10%2B5x-10%2Bx%5E2-2x-2x%29i%2B20-5

x%5E3%2Bx%5E2-17x%2B%282x%5E2%2B6x-20%29i%2B15

x%5E3%2Bx%5E2%2B%282+x%5E2%2B6+x-20%29i-17x%2B15