# $a,b,c$ are natural no and equations $x^2-5x+a=0,x^2-6x+b=0,x^2-8x+c=0$ have exactly one root in common and common root is also a natural no.$b+c$ is maximum when common root is :

$\begin{array}{1 1}(A)\;3&(B)\;4\\(C)\;3\;or\;4&(D)\;none\end{array}$

$b+c$ is maximum when common root is 3 or 4
Hence (C) is the correct answer.