According to the complex conjugate root theorem if f(x) is a polynomial in one variable with real coefficients, and x + yi is a root of f where x and y are real numbers, then its complex conjugate x − yi is also a root of f(x).

The complex conjugate of 2 - 5i is 2 + 5i.

The roots of f(x) are: 2 - 5i, 2 + 5i, and 3 with multiplicity 2.

We will use the property: If z is a zero of a polynomial, then (x-z) is a factor of the polynomial. Thus we can write:

f(x) =a(x - (2 - 5i))(x - (2 + 5i))(x - 3)^2

Simplifying we get the polynomial: :

f(x) = a*(x^4 - 10x^3 + 62x^2 - 210x + 261)