A) 3
B) 2
C) 1
D) 4
Correct Answer: B
Solution :
Let the roots of \[{{x}^{2}}-6x+a=0\] and the roots of \[{{x}^{2}}-cx+6=0\] be \[\alpha ,\,\,3\beta \] \[\therefore \,\,\alpha +4\beta =6\] ? (i) \[4\,\,\alpha \beta =a\] ? (ii) \[\alpha +3\beta =c\] ? (iii) and \[3\alpha \beta =6\] ? (iv) (ii) and (iv) \[\Rightarrow \,\,a=8\] \[\therefore \] 1st equation reduces to \[{{x}^{2}}-6x+8=0\] Clearly \[\alpha =2\] and \[\beta =1\] \[\therefore \] Common root is 2.
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