Question

How do you find a polynomial function with Degree: 6, Leading coefficient: 4, zeros: 3, 0 (multiplicity 3), and 2-3i?

Answer 1

`4 x^3 ( x - 3 ) ( ( x- 2 )^2 + 9 )=4 ( x^6- 7 x^5 - x^4 + 39 x^3)`

Explanation:

Complex roots occur in conjugate pairs. So, the not-in-the-list root is 2 + 3 i.
The polynomial is `4 x^3 ( x - 3 ) ( x- (2 = 3 i)) ( x + ( 2 - 3 i ))` = `4 x^3 ( x - 3 ) ( (x - 2 )^2 + 9)`