Question

Given a polynomial has roots -2,3, and 2i find the p(x)

Answer 1

start with
\[(x+2)(x-3)(x-2i)(x+2i)\] and then multiply out

Answer 2

\[(x+2)(x-3)\] should be routine, and \((x-2i)(x+2i)=x^2+4\)

Answer 3

i still dont get it.

Answer 4

if \(-2\) is a zero, then the polynomial has a factor of \(x+2\)

Answer 5

and if \(3\) is a zero, then another factor is \(x-3\)

Answer 6

etc

Answer 7

so what would the answer be

Answer 8

i don't know, i didn't do it. you have to multiply
\[(x+2)(x-3)(x^2+4)\] and see what you get

Answer 9

okay thanks

Answer 10

yw