Question

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

Answer 1

HI!!

Answer 2

you wanna do it the real quick way?

Answer 3

or the slow way?

Answer 4

Real quick please!

Answer 5

ok it is a matter of knowing that is \(a+bi\)is the root of a quadratic, it is
\[x^2-2ax+(a^2+b^2)\]

Answer 6

in your case \(a=-1,b=4\) so you get
\[x^2-2\times (-1)x+(-1)^2+4^2=x^2+2x+17\]

Answer 7

pretty quick huh?
you do have to memorize that though, there is a slower way to do it

Answer 8

So you just plug in the numbers into the equation? That's not bad at all

Answer 9

no it is not bad
make sure you know what \(a\) and \(b\) are , there is no \(i\) involved just
\[\huge x^2-2ax+a^2+b^2\]

Answer 10

bet $5 your teacher didn't mention it did they?

Answer 11

Haha no not at all! Thank you very much. I appreciate your help

Answer 12

\[\color\magneta\heartsuit\]