If a polynomial function with rational coefficients has the zeros -3+sqrt5, -i, what are the additional zeros?
1 Answer
Mar 3, 2017
Explanation:
Complex zeros always come in pairs:
The pairs form a quadratic equation:
-
(x+3-sqrt(5))(x+3+sqrt(5)) = x^2 + 3x +sqrt(5)x + 3x + 3sqrt(5) - sqrt(5)x -3 sqrt(5) - sqrt(5) sqrt(5) = x^2+ 6x - 5 -
(x-i)(x+i) = x^2 + x i -x i -i^2 = x^2 +1 ,
Note:i^2 = -1
In summary: The additional zeros are