SOLUTION: Two roots of a polynomial equation with real coefficients are 2+3i and square root of 7. Then find two additional roots. Then find the degree of the polynomial.

Algebra ->  Rational-functions -> SOLUTION: Two roots of a polynomial equation with real coefficients are 2+3i and square root of 7. Then find two additional roots. Then find the degree of the polynomial.      Log On


   

Question 253818: Two roots of a polynomial equation with real coefficients are 2+3i and square root of 7. Then find two additional roots. Then find the degree of the polynomial.
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
FIrst we are given 2 roots:
2%2B3i
and
+sqrt%287%29.
The other 2 roots are
2-3i
and
-sqrt%287%29
These are both conjugates.
So, we have a polynomial expressed as
%28x-%282%2B3i%29%29%28x-%282-3i%29%29%28x-sqrt%287%29%29%28x%2Bsqrt%287%29%29
this can be simplified to
%28x%5E2-4x+%2B+13%29%28x%5E2-7%29
and then to
x%5E4-4x%5E3%2B6x-91