Write a polynomial function with rational coefficients so that p (x) = 0 has the given roots: - 5 and 3i

For a polynomial with ratinal coefients, if a+bi is a root, then a-bi is a root

since 0+3i is a root, 0-3i is also a root

if the roots of an equtation are r1, r2, r3, the factored form of the polynomial is like this

(x-r1) (x-r2) (x-r3)

given

roots are - 5, 3i and - 3i

(x - (-5)) (x-3i) (x - (-3i)) or

(x+5) (x-3i) (x+3i)

if we expand

x³+5x²+9x+45