Find a Polynomial

Question

Find a polynomial of degree 5 with zeros 3, 2, -5, and -i. [You may leave in factored form as linear and irreducible quadratic factors]

Answer 1

Assuming you also want real coefficients (which should be stated in the problem), the complex conjugate of any complex zero must also be a zero, so you will have 5 zeros:

3

2

-5

-i

i

Then

p(x) = A(x - 3)(x - 2)(x + 5)(x + i)(x - i) = A(x - 3)(x - 2)(x + 5)(x² + 1)

where A is real and A≠ 0.