Question

write a polynomial function of least degree that has real coefficeints the given zeros and a leading coefficient of 1. the problem is 5,2i,-2i

Answer 1

*i think you mean the ZEROS / ROOTS are 5, 2i and -2i.

if so, you can get them by multiplying and expanding,
(x-5)(x-2i)(x+2i)
note that 1 = sqrt(-1)

but an easier method would be, to start with the roots 2i and -2i. recall that q quadratic equation follows the formula,
x^2 - (sum of roots)*x + (product of roots)
thus, substituting 2i and -2i:
x^2 - (2i - 2i)*x + (2i)*(-2i)
x^2 - (0)*x - 4*(i^2)
x^2 - 4*(-1)
x^2 + 4
now, we multiply this by (x-5):
(x-5)(x^2 + 4)
x^3 - 5x^2 + 4x - 20

hope this helps~ :)