If is a polynomial function of degree then has excatly linear factors and

Where is some non zero real number

            are the complex zeros of .

The zeros are .

Because is zero and the polynomial is to have real coefficients, must also be a zero.

Using the linear factorization therom and the zeros we can write as follows.

.

While can be any non zero real number, it is simplest to let .

Then write the function in the standard form.

.

Therefore, a function of least degree that has as zeros is

  or any non multiple of .

.