Question

Degree 4; zeros: -4+5i, -1 multiplicity 2

Answer 1

`f(x) = [x^(2) + 8x + 41](x + 1)^(2)`

Explanation:

If -4 + 5i is a root of a polynomial, then it's conjugate -4 - 5i will also be a root of the same polynomial.

Therefore, the polynomial has 4 degree, and zeroes are (- 4 + 5i), (- 4 - 5i) and -1 with multiplicity 2.

Hence, the polynomial will be

`f(x) = (x + 4 - 5i)(x + 4 + 5i)(x + 1)^(2)`

⇒
`f(x) = [x^(2) + 8x + (4 - 5i)(4 + 5i)] (x + 1)^(2)`

⇒
`f(x) = [x^(2) + 8x + 41](x + 1)^(2)` (Answer)