Question

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

will give medal!!

Answer 1

you want a real quick method?

Answer 2

yes that would be nice :)

Answer 3

if \(a+bi\) are the roots of a quadratic, then the quadratic is
\[x^2-2ax+(a^2+b^2)\]

Answer 4

in your case
\[a=1,b=4\] so the quadratic is
\[x^2-2\times (-1)x+(1^2+4^2)\] or
\[x^2+2x+17\]

Answer 5

sorry i meant \(a=-1,b=4\) but the answer i wrote is correct
if you cannot memorize that, another method is to work backwards
\[x=-1+4i\]
\[x+1=4i\]
\[(x+1)^2=(4i)^2=-16\]
\[x^2+2x+1=-16\]
\[x^2+2x+17=0\]

Answer 6

oh! okay thank you :)

Answer 7

yw
easy right?

Answer 8

i guess i just made it so much harder than it was! :)

Answer 9

worst method is to try to multiply out
\[(x-(-1+4i))(x-(-1-4i))\] you will get stuck somewhere and likely make a mistake