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$a,b,c$ 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.The common root is :

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

Can you answer this question?

Common root is a natural no and sum of roots is also a natural no.
$\therefore$ D must be a perfect square for all equations.
The common root is 1 or 2 or 3 or 4
Hence (D) is the correct answer.
answered Apr 15, 2014