Question 385897
Divide both sides by a:  {{{x^2 + bx/a + c/a = 0}}}.  If one root is 5+i then 5 - i is also a root.  Then {{{-b/a = 5+i + 5 - i = 10}}}, or b = -10a.  Also, {{{c/a = (5+i)(5 - i) = 25 -i^2 = 26}}}, or c = 26a.  Therefore {{{ax^2+bx+c=ax^2 - 10ax + 26a = 0}}}, or {{{x^2 - 10x + 26 = 0}}}, after dividing by a.