SOLUTION: degree 3 with zeros of -2 and 5+i

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Question 1135762: degree 3 with zeros of -2 and 5+i
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

degree 3
zeros of:
x%5B1%5D=+-2+
x%5B2%5D=5%2Bi-> since complex roots come in pairs, you also have x%5B3%5D=5-i

use zero product theorem to find f%28x%29

f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29
f%28x%29=%28x-%28-2%29%29%28x-%285%2Bi%29%29%28x-%285-i%29%29
f%28x%29=%28x%2B2%29%28x-5-i%29%28x-5%2Bi%29
f%28x%29=%28x%2B2%29%28x%5E2-5x%2Bix-5x%2B25-5i-ix%2B5i-i%5E2%29
f%28x%29=%28x%2B2%29%28x%5E2-10x%2B25-%28-1%29%29
f%28x%29=%28x%2B2%29%28x%5E2+-+10+x+%2B+26%29
f%28x%29=+x%5E3+-+10+x%5E2+%2B+26x%2B2x%5E2-20x%2B52
f%28x%29=+x%5E3+-+8x%5E2+%2B+6x%2B52