Question

Find a quadratic equation with roots -1+4i and -1-4i.

I have absolutely no clue where to even start. Please teach me how to do this?

Answer 1

Have u tried Khan academy?

Answer 2

Briefly, but to no avail. @selrachcw95

Answer 3

If those are the roots, then when we plug those values in for x...the quadratic has to equal 0. The way we insure our quadratic will equal zero is to set it up like this:
(x - (-1+4i))(x - (-1-4i)) = 0
Now, FOILing that out is kind of a pain, but that's how you start.

Answer 4

I'm foiling it out right now. What do I do after it's foiled? @BangkokGarrett

Answer 5

Getting rid of some of those parenthesis, we just need to foil out this.
(x + 1 - 4i)(x + 1 + 4i)
After foiling, just simplify as much as possible and you should have a quadtratic

Answer 6

The i terms should go away. There will be a term with i^2 in it, but remember i^2 is just -1

Answer 7

My foiling is definitely not going right, I keep ending up with just a number & an x. I've got 32x twice and something else a first time. @BangkokGarrett

Answer 8

(x + 1 - 4i)(x + 1 + 4i)
x^2 + x + 4ix + x + 1 + 4i - 4ix -4i -16i^2
x^2 + x + x + 1 -16i^2
x^2 + 2x + 1 + 16
x^2 + 2x + 17

Answer 9

On the 2nd line + 4ix - 4ix cancels and + 4i - 4i cancels

Answer 10

I see where I screwed up now, I wasn't doing it in order. So that would be my answer? Thank you so much!

Answer 11

Gave ya a medal!