Question

write the quadratic equation whose roots are 2-1i and 2+1i

Answer 1

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

Answer 2

if this is too much to memorize, you can also do this by working backwards,
\[x=2+i\\
x-2=i\\
(x-2)^2=i^2=-1\\
x^2-4x+4=-1\\
x^2-4x+5=0\]

Answer 3

thank you!