Question

write a fourth degree polynomial function in standard form with zeros 2+i, 2, -1

Answer 1

the zeros have to be \(2+i\) and its conjugate \(2-i\) also \(2\) and \(-1\)
the second two tell you that there are factors \((x-2)\) and \((x+1)\)

Answer 2

to come up with a quadratic (degree 2) with zeros \(2+i\) and \(2-i\) is not hard, there are a couple ways to do it
one is pretty easy, the second is instantaneous but it requires memorizing something

Answer 3

do you know how to do it?

Answer 4

ya i think i know now

Answer 5

thanks

Answer 6

one thing you probably do not want to do is multiply
\[(x-(2+i))(x-(2-i))\] because that is a real pain

Answer 7

i mean it will work, but it is a pain none the less
the memorizing way is to know that if \(a+bi\) is the root of a quadratic, then the quadratic is
\[x^2-2ax+(a^2+b^2)\]
if you memorize that you get your answer instantly