If (2+4 i ) is one of the roots of (x^2+b x+c=0 ) with (b, c R ) then ((b, c)= )

Step-by-step solution

It is given that (2+4 i ) is one of the roots of (x^2+b x+c=0 ) with (b, c R ), so other root will be (2-4 i ). Now, the sum of roots (=-b ) ( (2+4 i)+(2-4 i)=-b b=-4 ) and the product of roots (=c ) ( aligned & (2+4 i)(2-4 i)=c & 4+16=c c=20 & (b, c)=(-4,20) aligned ) Hence, option (d) is correct.