SOLUTION: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 8, -14, and 3 + 9i

Algebra ->  Rational-functions -> SOLUTION: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 8, -14, and 3 + 9i      Log On


   

Question 764823: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
8, -14, and 3 + 9i
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The other needed zero is 3-9i, because complex zeros come in conjugate pairs.

Your function in a form other than general (here being factored) will be
p%28x%29=%28x-8%29%28x%2B14%29%28x-%283%2B9i%29%29%28x-%283-9i%29%29

You asked for "real coefficients" and in "standard form". In keeping with that, you probably want the quadratic factor corresponding to the two complex factors containing imaginary components.

%28x-3-9i%29%28x-3%2B9i%29=%28x-3%29%5E2-%289i%29%5E2=x%5E2-6x%2B9%2B81=x%5E2-6x%2B90
Finally without showing any complex numbers plainly, your standard form function if other than general form, is highlight%28p%28x%29=%28x-8%29%28x%2B14%29%28x%5E2-6x%2B90%29%29