m is a degree 5 polynomial that passes through the origin, has zeros i and 5 − i , and m ( − 2 ) = − 2500 . Find the equation for m

Answer 1

x=5-i

x-5 = -i

(x-5)^2 = (-i)^2 = 1

x^2 -10x +25 = 1

x^2-10x +24 = 0

x(x^2+1)(x^2-10x+24) has zeros 0,i, -i, 5-i, and 5+i. It's 5th degree.

= x^5 -10x^4 +25x^3 -10x^2 + 24x

sort of like doing a 3 dimensional FOIL,