Question

Find all degree 5 polynomials with real coefficients if 4+i and 5(multiplicity 3) are zeros.

Answer 1

one factor is evidently \((x-5)^3\) right?

Answer 2

or not?

Answer 3

yes

Answer 4

so you need the quadratic right?

Answer 5

yes

Answer 6

the easy method is this: if \(a+bi\) is a zero of a quadrtic, then the quadratic is
\[x^2-2ax+a^2+b^2\]or a multiple if it