Question

Given f(x) = 2x^3+3x^2+50x+75, and the zero 5i, find the other zeros?

Answer 1

because these are real number coefficents, we immediately know 1 other zero is -5i

Answer 2

5i, -5i, -3/2

Answer 3

way to use that calculator

Answer 4

how do you find -3/2 though?

Answer 5

synthetic division

Answer 6

yeah, I know about the conjugate, what would you divide by?

Answer 7

divide by x-5i

Answer 8

want me to show it here?

Answer 9

please? because we never divided by i's in class. :/

Answer 10

ok, my writing is kind of messy

Answer 11

if one zero is 5i, then the other one is -5i so this factors as
\[(x-5i)(x+5i)\times\text{something})\] and so
\[(x^2+5)(\text{something})\] you can find the something by divison, or by thinking

Answer 12

sorry that was wrong, it is
\[(x^2+25)(\text{something})\]