Question

Find Polynomial of lowest degree whose zeros are 3,2,and 5i. show work and write answer in standard form

Answer 1

Welcome to Open Study, Lanie!

That imaginary root, 5i, complicates things around here!

Why don't we begin by finding the polynomial of lowest degree whose zeros are just {3,2}.

The corresponding factors of the polynomial have the opposite signs: (x-3) and (x-2).

Multiplying these together results in f(x) = x^2 - 5x + 6.

That's a polynomial of lowest degree for zeros {3,2}.


Please consider now what we'd do, additionally, if another zero were 5i. What would the corresponding factor be?

It'd be unusual to have one imaginary zero; I'd expect that there be 5i and its comjugate, -5i. What would the corresponding factors be?

Try putting all this info together to obtain the desired polynomial.