Question 187719
{{{x=4+i}}} or {{{x=4-i}}} Start with the given roots.



{{{x-4=i}}} or {{{x-4=-i}}} Get the real numbers to the left side.



{{{(x-4)^2=(i)^2}}} or {{{(x-4)^2=(-i)^2}}} Square both sides.



{{{(x-4)^2=-1}}} or {{{(x-4)^2=-1}}} Square "i" to get -1. Square "-i" to get -1.  



Since these equations are identical, this means that we can use one equation



{{{(x-4)^2=-1}}} 



{{{x^2-8x+16=-1}}} FOIL the left side



{{{x^2-8x+16+1=0}}} Add 1 to both sides.



{{{x^2-8x+17=0}}} Combine like terms.




So the quadratic equation that has the roots 4+i and 4-i is {{{y=x^2-8x+17}}}