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

will give medal!!

Question

find a quadratic equation with roots -1+4i and -1-4i

will give medal!!

anonymous · Answer

you want a real quick method?

anonymous · Answer

yes that would be nice :)

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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 
$$x=-1+4i$$
$$x+1=4i$$
$$(x+1)^2=(4i)^2=-16$$
$$x^2+2x+1=-16$$
$$x^2+2x+17=0$$

anonymous · Answer

oh! okay thank you :)

anonymous · Answer

yw
easy right?

anonymous · Answer

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

anonymous · Answer

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