SOLUTION: Find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.) Thanks! 6, 7 + i

Algebra ->  Functions -> SOLUTION: Find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.) Thanks! 6, 7 + i      Log On


   

Question 1006537: Find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.) Thanks!
6, 7 + i
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
p(x) = (x-6)*(x-(7+i))*(x-(7-i)) = (x-6)*(x^2 - 14x + 50).

It is based on two theorems.

First theorem says:
"If a polynomial with real coefficients has a complex root (the root which is complex number)
then it has the root which is complex conjugate to the first one".

Second theorem says:
"If a polynomial p(x) of degree n with the leading coefficient 1 at x%5En has n roots x%5B1%5D, x%5B2%5D, . . . , x%5Bn%5D,
then the polynomial is p(x) = %28x+-+x%5B1%5D%29*%28x+-+x%5B2%5D%29* . . . *%28x-x%5Bn%5D%29.