SOLUTION: Find a polynomial with the lowest degree, with real coefficients whose zeros include, 4,-10, 3+4i I've gone through the problem and i dont have an answer that matches the choices

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: Find a polynomial with the lowest degree, with real coefficients whose zeros include, 4,-10, 3+4i I've gone through the problem and i dont have an answer that matches the choices       Log On


   

Question 966814: Find a polynomial with the lowest degree, with real coefficients whose zeros include, 4,-10, 3+4i
I've gone through the problem and i dont have an answer that matches the choices im not sure if i did it wrong or if the paper is incorrect so checking here!
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-4%29%28x-%28-10%29%29%28x-%283%2B4i%29%29%28x-%283-4i%29%29

%28x-4%29%28x%2B10%29%28x-3-4i%29%28x-3%2B4i%29

%28x-4%29%28x%2B10%29%28%28x-3%29-4i%29%28%28x-3%29%2B4i%29

%28x-4%29%28x%2B10%29%28%28x-3%29%5E2-%284i%29%5E2%29

%28x-4%29%28x%2B10%29%28x%5E2-6x%2B9-16i%5E2%29, and remember, i%5E2=-1;

%28x-4%29%28x%2B10%29%28x%5E2-6x%2B9%2B16%29

%28x-4%29%28x%2B10%29%28x%5E2-6x%2B25%29

Still not yet in general form, but you see the main process. The three given zeros, one of them being complex, you need also the conjugate of that complex zero; so FOUR zeros for the polynomial. Setup the factors, and the rest is algebraic steps.