# How do you write a polynomial function of least degree that has real coefficients, the following given zeros 3-i,5i and a leading coefficient of 1?

##### 1 Answer

Dec 10, 2016

Any polynomial with real coefficients and imaginary or complex zeros, must have zeros that are conjugate pairs, therefore, the polynomial must have the following factors:

Multiplying the last two factors is easy; it is the sum of two squares:

Multiplying the first two factors is a bit more difficult:

Combine like terms:

Use the identity

Multiply the remaining factors:

Combine like terms: