What is the polynomial of the Degree is 4; zeros is 2, multiplicity is 2,3i

Degree is 4

ok so

remember that multiplicity is how many times the root repeats

whenever you have a polynomial with real coefients and have a root that is a+bi, then a-bi is also a root

since 3i is a root, - 3i is also a root

so

if the roots are r1, r2, r3, r4, then the factored form is (x-r1) (x-r2) (x-r3) (x-r4)

2 is mulitplicty 2 and the other 2 roots are 3i and - 3i

(x-2) ² (x-3i) (x - (-3i))

(x-2) (x-2) (x-3i) (x+3i)

if we expand

the polynomial is x⁴-4x³+13x²-36x+36