Let the roots of equation x2−6x+a=0 be α and 4 β and that of the equation x2−cx+6=0 be α and 3β.Then α+4β=6... (i) 4αβ=a... (ii) and α+3β=c... (iii) 3αβ=6...(iv) ⇒a=8( from (ii) and (iv)) ∴ The equation becomes x2−6x+8=0 ⇒(x−2)(x−4)=0 ⇒ roots are 2 and 4 ⇒α=2,β=1∴ Common root is 2