Question

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

Answer 1

Can someone please explain this to me step by step im so lost :(

Answer 2

If p and q are the roots of a quadratic equation,
then the quadratic equation will be: (x - p)(x - q) = 0

Answer 3

Therefore, multiply and set it to zero:
{ x - (-1 + 4i) } * { x - (-1 - 4i) } = 0
Simplify.
Remember i^2 = -1

Answer 4

Im so lost:(

Answer 5

I need someone to show me this step by step i haven't done this in a really long time so i dont remember anything im so sorry

Answer 6

I typed a whole bunch of stuff and the page refreshed automatically and I lost everything :(

Answer 7

I will type it in Notepad and copy and paste it here. Give me a couple of minutes.

Answer 8

Okay i appreciate this very much <3 so sorry :(

Answer 9

{ x - (-1 + 4i) } * { x - (-1 - 4i) }
Get rid of the inside parenthesis by distributing the negative sign
(x + 1 - 4i) * (x + 1 + 4i)
Take the first term x on the left and multiply each term on the right with it:
x^2 + x + 4xi
Take the second term 1 on the left and multiply each term on the right with it:
x + 1 + 4i
Take the third term -4i on the left and multiply each term on the right with it:
-4xi - 4i - 16i^2 = -4xi - 4i + 16 (because i^2 = -1)

Add up all three products:
x^2 + x + 4xi + x + 1 + 4i + -4xi - 4i + 16
simplify
x^2 + 2x + 17 = 0 is the quadratic equation.

Answer 10

And that is the answer? Btw. Thank you so much you are a life saver :)