Question

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

Answer 1

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