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20 14 national junior high school mathematics league, the fifth question in the preliminary round of the third grade group, how to do it?
You copied the question wrong, because the quadratic function y=x2+ax+b image passes through points A (x 1, 0), B (x2, 0) and C (2, m), 0 < x 1 < x2 < 2.

(1) verification: m > 0;;

(2) If b≥ 1, verify M < 1.

It is proved that: (1) from the known y=(x-x 1)(x-x2), substitute C(2, m) into y=(x-x 1)(x-x2) and get m = (2-x/klx2). 0, (2-x2)>0, so m>0.

(2) The relationship between root and coefficient is known as x 1x2 = b and m = (2-x 1) (2-x2), so BM = x1x2 (2-x1) =/.

(1-(x1-1) 2) (1-(x2-1) 2), because? (1-(x 1- 1) 2) is greater than 0, less than or equal to 1, (1-(x2- 1) 2) is greater than.

0, less than or equal to 1, but not at the same time 1, so

(1-(x1-1) 2) is less than1because b≥ 1,

So m < 1