Write a polynomial function of lowest degree with rational c

Write a polynomial function of lowest degree with rational coefficients that has – 3 and – i as some of its zeros. Start by using theorems about zeros of polynomial functions to identify any other zeros.

Solution

Dear Student

Given a polynomial with zeroes as -3 and -i.

Now since complex roots always occur in pair , therefore if -i is a root of the polynomial then +i should also be root.

Therefore the polynomial of lowest degree should be of the form

(x-i)(x+i)(x+3) = 0

(x^2 +1)(x+3) = 0

x^3 + 3x^2 + x + 3 = 0

Solution