If 1+2i  is a root of the equation x2+bx+c=0;   b,c∈R,  then (b,c)  is given by

The given equation is x2+bx+c=0 , coefficients are real Given that one root is 1+2i Let other root is 1−2i Sum of the roots : (1+2i)+(1−2i)=−b ⇒b=−2 Product of the roots : (1+2i)(1−2i)=c ⇒c=5 (b,c) = (−2,5)