2

2

(I have seen this kind of question, and they actually ask the minimum value of 3a+b.... )

QE: ax^{2 }+ bx + 6 = 0

Since the Quadratic Equation has no distinct roots, so b^{2} = (4)(a)(6)

Or,

The minimum value of this will clearly be -2 (when b = -4 and 3a = 2, or a=2/3)