SOLUTION: Two zeros of a polynomial are 3-4i and 1+i. What is the lowest possible degree of the polynomial. I believe the quadratic equation would be x^2+xi-4x+5-i.

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Question 1088043: Two zeros of a polynomial are 3-4i and 1+i. What is the lowest possible degree of the polynomial. I believe the quadratic equation would be x^2+xi-4x+5-i.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
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Two zeros of a polynomial are 3-4i and 1+i. What is the lowest possible degree of the polynomial. I believe the quadratic equation would be x^2+xi-4x+5-i.
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Lowest possible degree for the polynomial is 4. Why? Complex zeros occur as conjugate pairs.

%28x-%283-4i%29%29%28x-%283%2B4i%29%29%28x-%281%2Bi%29%29%28x-%281-i%29%29

Steps to simplify:
%28x-3%2B4i%29%28x-3-4i%29%28x-1-i%29%28x-1%2Bi%29
%28%28x-3%29%2B4i%29%28%28x-3%29-4i%29%28%28x-1%29-i%29%28%28x-1%29%2Bi%29
%28%28x-3%29%5E2%2B16%29%28%28x-1%29%5E2%2B1%29------used knowledge of difference of squares
%28x%5E2-6x%2B9%2B16%29%28x%5E2-2x%2B1%2B1%29
...continue simplifying and then doing the multiplication...
but you see the degree is 4
.
.

Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
If polynomials with complex coefficients are good for you, then the lowest possible degree is 2.

If you want to have the polynomial with REAL coefficients, then the lowest possible degree is 4.


But you said NOTHING about in which set of polynomials do you search for the solution, and this creates
the problem (= unanswered question) for us, the tutors.