math polynomial function

Question

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the polynomial in standard form.

3i, 2−i

Answer 1

There are four zeros: ±3i, 2±i.  These are also known as the roots of some polynomial.

 

Now construct the polynomial in factored form: (x-root)(x-root)(x-root)(x-root) = 0 where each "root" is a different one from the known four.

 

Then all you have to do is multiply it out.  Hint (x-2i)(x+2i) = x²+4