Question

Can anyone please help me ?

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

Answer 1

there are a couple ways to do this, one is to work backwards
\[x=-1+4i\]
\[x+1=4i\]
\[(x+1)^2=-16\]
\[x^2+2x+1=-16\]
\[x^2+2x+17=0\]

Answer 2

another way is to memorize that if \(a+bi\) is the zero of a quadratic, then the quadratic is
\[x^2-2ax+(a^2+b^2)\]

Answer 3

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

Answer 4

oops i meant \(x^2+2x+17\) as before

Answer 5

Oh my Thank you for explaing it step by step !

The final answer would be x^2+2x+17 right ?

Answer 6

@satellite73 ?