Degree 4; zeros: 4-5i; 5 multiplicity 2

Question

Form a polynomial f(x) with real coefficient having the given degree and zeros

Answer 1

If 4-5i is a zero, its complex conjugate lust also be a zero. This gives 2 factors:

(x-4-5i)(x-4+5i)

The additional 2 zeros are (x-5)(x-5) because the multiplicity is 2.

So the factored form for this polynomial is: y=(x-4-5i)(x-4+5i)(x-5)(x-5)

***You need to multiply the factors together to get the final polynomial.