SOLUTION: Form a​ third-degree polynomial function with real coefficients such that 6 plus i and 7 are zeros

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Question 1126930: Form a​ third-degree polynomial function with real coefficients such that 6 plus i and 7 are zeros
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

if x%5B1%5D=6+%2Bi and x%5B2%5D=7 are given zeros, there must be also zero x%5B3%5D=6+-i because complex zeros always coming in pairs
use zero product formula:
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29
f%28x%29=%28x-%286+%2Bi%29%29%28x-7%29%28x-%286+-i%29%29
f%28x%29=%28x-6+-i%29%28x-7%29%28x-6+%2Bi%29
f%28x%29=%28x%5E2-6x+-xi-7x%2B42%2B7i%29%28x-6+%2Bi%29
f%28x%29=%28x%5E2-13x+-xi%2B42%2B7i%29%28x-6+%2Bi%29
f%28x%29=%28x%5E2-%2813+%2Bi%29x%2B7%286%2Bi%29%29%28x-6+%2Bi%29
f%28x%29=x%5E3+-+19+x%5E2+%2B+121x+-+259