question_answer

If \[\alpha \] & \[\beta \] are the zeroes of the quadratic polynomial \[3{{x}^{2}}-11x+6,\] then find the polynomial whose zeroes are \[(2\alpha +\beta )\] and \[(\alpha +2\beta )\]

A)  \[k\,\,\left( {{x}^{2}}-5x+\frac{270}{9} \right)\], \[k\] is any non-zero real number

B) \[k\,\,\left( {{x}^{2}}-11x+\frac{260}{9} \right)\], \[k\] is any non-zero real number

C) \[k\,(3{{x}^{2}}-3x+26),\] \[k\] is any non-zero real number

D) \[k\,(2{{x}^{2}}-5x+27),\] \[k\] is any non-zero real number

E)  None of these