Given the quadratic function y = ax ^ 2 + BX + C (a ≠ 0), when x = 1 / 2, the maximum value of this function is 25,

Because when x = 1 / 2, the maximum value of this function is 25, so (α + β) / 2 = 1 / 2, and because α ^ 2 + β ^ 2 = 19, we can get α ^ 2 - α - 9 = 0, similarly β ^ 2 - β - 9 = 0, and because a / 4 + B / 2 + C = 25, - B / 2A = 1 / 2, we can get b = - A, C = 25 + A / 4, and because a α ^ 2 + B α + C = 0, so a * (α ^ 2 - α) + C = 0, we can get C = - 9A

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