Math help!!?

Question

Write a polynomial function with the zeros of x= -1, 2, and 2i 

Answer 1

The zeros of a polynomial function are x = -1 , 2 , 2i

Since the coefficients of a polynomial function are Real Numbers and 2i is a zero,- 2i must also be a zero.

Now the total zeros of a polynomial function are x = -1, 2 , 2i , -2i.

Let a = -1 , b = 2 , c = 2i , d = -2i

Polynomial function = (x-a)(x-b)(x-c)(x-d) = (x-(-1))(x-2)(x-2i)(x-(-2i)) = (x+1))(x-2)(x-2i)(x+2i)

= (x²+1x-2x-2*1) (x² - (2i)²) = (x²-x-2) (x² - 4(-1)) = (x²-x-2) (x² + 4)

= (x²)(x²) - x(x²) - 2(x²) + (4)(x²) - x(4) - 2(4)

= x⁴ - x³ - 2x² + 4x² - 4x - 8 = x⁴ - x³ + 2x² - 4x - 8.

Solution : Requied polinomial function is x⁴ - x³ + 2x² - 4x - 8.