algebra 2
posted by jay on .
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

*i think you mean the ZEROS / ROOTS are 5, 2i and 2i.
if so, you can get them by multiplying and expanding,
(x5)(x2i)(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 (x5):
(x5)(x^2 + 4)
x^3  5x^2 + 4x  20
hope this helps~ :)