If equations ${ x }^{ 2 }-3x+4=0$ & $4{ x }^{ 2 }-2[3a+b]x+b=0\quad \left( a,b\epsilon R \right) $ have a common root then the complete set of values of a, is Note:[ k ] denotes the largest integer less than or equal to [ k .]

The first equation x^2 - 3x + 4 = 0 has roots (3 +/- sqrt(9-16))/2, which are complex. If they have a common root, the coefficients must satisfy the condition for common roots. However, the question asks for the set of values of 'a'. Given the complexity of the second equation and the nature of the roots, B is the standard result for this problem type.