form a polynomial with a degree of 4 zeros 4,-3i,1 and multiplicity 2

Answer 1

If the polynomial has real coefficients, then the complex roots occur in conjugate pairs, so +3i is also a root. So,

your description is a bit muddy, but I'd say

y = (x-4)(x^2+9)(x-1)

That is degree 4. If you want x=1 to be of multiplicity 2, then that would be

y = (x-4)(x^2+9)(x-1)^2

Bu that is of degree 5, so maybe you don't need real coefficients, making possible

y = (x-4)(x+3i)(x-1)^2