Find a polynomial with integer coefficients that satisfies the given conditions. r has degree 4 and zeros 3 − 3i and 2, with 2 a zero of multiplicity 2

The required polynomial is .

Step-by-step explanation:

If a polynomial has degree n and are zeroes of the polynomial, then the polynomial is defined as

It is given that the polynomial R has degree 4 and zeros 3 − 3i and 2. The multiplicity of zero 2 is 2.

According to complex conjugate theorem, if a+ib is zero of a polynomial, then its conjugate a-ib is also a zero of that polynomial.

Since 3-3i is zero, therefore 3+3i is also a zero.

Total zeroes of the polynomial are 4, i.e., 3-3i, 3_3i, 2,2. Let a=1, So, the required polynomial is

Therefore the required polynomial is .