Question

Find the fourth-degree polynomial function with zeros 2, -2, 2i, and -2i. Write the function in factored form.

Answer 1

x= root
(x-root) is a factor of equation
factor*factor*factor*factor = fourth degree polynomial

Answer 2

I don't understand. @FaiqRaees

Answer 3

recall when you solved something like

x^2 + 3x + 2 = 0
(x + 1)(x + 2) = 0

you factored like that, and then set each quantity =0 to solve for x

Answer 4

do that backwards here, they gave you the x values for this thing, make quantities that will equal zero with those x values...
like
(x - 2i)

+2i will make that zero

Answer 5

So, it will be something like: x(x+2)(x-2)(x+2i)(x-2i)?
sorry, i'm new at this and really bad at it

Answer 6

@DanJS

Answer 7

yes good, but the x in front says that x=0 would be a root,

Answer 8

Alright. So no x in front.

Answer 9

(x+2)(x-2)(x+2i)(x-2i) = 0

that is good enough for me, they prolly want it in

ax^4 + bx^3 + cx^2 + dx + e = 0

so you would have to multiply it all out

Answer 10

(x^2 - 4) ( x^2 - 4i^2) = 0

(x^2 - 4) ( x^2 - 4*(-1)) = 0


(x^2 - 4) ( x^2 + 4) = 0

Answer 11

It was right! Wow. That was a lot easier then I thought.

Answer 12

Thank you so much!