$a,b,c$ 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.$(a+b+c)$ is minimum when common root is :

Question

$\begin{array}{1 1}(A)\;1&(B)\;2\\(C)\;3&(D)\;4\end{array} $

Answer 1

$a,b,c$ 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.$(a+b+c)$ is minimum when common root is 1

Hence (A) is the correct answer.