Question

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

Answer 1

Find*

Answer 2

(x - root)(x - root), so you need to mulitply

\[(x + 1 - 4i)(x+1+4i)\]
When you do the imaginary parts will cancel and you'll have the quadratic

Answer 3

@peachpi is right

Answer 4

I still don't understand it very well... i'm sorry @peachpi

Answer 5

do you know how to foil?

Answer 6

No not very well @peachpi

Answer 7

that's ok. basically it's just applying the distributive property. You take each term from the 1st parentheses and multiply it by each term in the second.

Starting with the \(x\) in the 1st, multiply and get
\(x(x+1+4i)=x^2+x+4ix\)

You try it with the 2nd and third terms. Just distribute.
2nd: \(1(x+1+4i)=\)
3rd: \(-4i(x+1+4i)=\)

Answer 8

2nd: x+1+4i
3rd: -4ix-4i-16i
right? @peachpi

Answer 9

The second one is right. The third is almost right.
-16i should be -16i².
Then because \(i^2=-1\), it reduces to 16.
Altogether is should be \(-4ix-4i+16\)
Make sense?

Answer 10

Yep makes sense now! @peachpi

Answer 11

so now all you have to do is add up what we got from the multiplication for each step. Every term with an i will cancel, and then combine everything else to get the final answer

Answer 12

Okay thanks so much @peachpi