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If $a, b, c \in N$ and the equations $x^{2} - 5 x + a = 0$ , $x^{2} - 6 x + b = 0$ , $x^{2} - 8 x + c = 0$ have exactly one root common and the common root is a natural number

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If a,b,c∈N and the equations x2−5x+a=0 , x2−6x+b=0 , x2−8x+c=0 have exactly one root common and the common root is a natural number