Write a polynomial function in standard form with the given zeros 4 and -3i.

Answer 1

(x+3i)(x-4) = x^2 - 3ix -4x -12i

= x^2 -(4+3i)x - 12i a quadratic polynomial

unless you require real coefficients of the variables

then add in another factor (x-3i), the conjugate to get

(x+3i)(x-3i)(x-4) , cubic polynomial

Answer 2

3i also zero because polynomial must be with real coefficients. So, in factored form we have

f(x) = (x - 4)(x + 3i)(x - 3i)= (x - 4)(x² + 9) = x³ - 4x² + 9x - 36