SOLUTION: Help please! :( Form a polynomial f(x) with real coefficients having the given degree and zero. Degree: 4; zeros: 4+5i; 5 multiplicity 2 So far, I have done gotten this far (not

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Help please! :( Form a polynomial f(x) with real coefficients having the given degree and zero. Degree: 4; zeros: 4+5i; 5 multiplicity 2 So far, I have done gotten this far (not      Log On


   

Question 852802: Help please! :( Form a polynomial f(x) with real coefficients having the given degree and zero. Degree: 4; zeros: 4+5i; 5 multiplicity 2
So far, I have done gotten this far (not sure if it is completely correct):
f(x)=a[x-(5)][x-(5)][x-(4-5i)][x-(4+5i)]
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Your arrangement is correct. You would not need the factor "a" unless you need to fit some further fact about the needed function. For your purposes, a=1.

Just know that your factors with the imaginary numbers need to be arranged so that your multiplication process can take advantage of the difference between squares.

%28x-%284-5i%29%29%28x-%284%2B5i%29%29
%28x-4%2B5i%29%28x-4-5i%29
%28%28x-4%29%2B5i%29%28%28x-4%29-5i%29
%28x-4%29%5E2-%285i%29%5E2
%28x-4%29%5E2-25%2Ai%5E2
%28x-4%29%5E2-%28-1%2925
%28x-4%29%5E2%2B25
. not finished, but not expected difficult
.
.