If a and b are integers such that 2x2&nbsp;&minus; ax + 2 ＞ 0 and x2&nbsp;&minus; bx + 8 &ge; 0 for all real numbers x, then the largest possible value of 2a &minus; 6b is

If a and b are integers such that 2x² − ax + 2 ＞ 0 and x² − bx + 8 ≥ 0 for all real numbers x, then the largest possible value of 2a − 6b is

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