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Mathematics module (1)
Solution: (1) set points A (x 1, 0) and B (x2, 0), then x 1, x2 is the two roots of the equation x2-mx+m-2=0.

∫x 1+x2 = m,x 1? X2 = m-2 < 0, that is, m < 2,

ab = | x 1-x2 | =(x 1+x2)2-4x 1x 2 =

5,

∴m2-4m+3=0.

Solution: m= 1 or m=3 (truncation),

The value of∴ m is 1.

(2) Let M(a, b), then N(-a, -b).

∵M and n are two points on a parabola,

∴-a2+ma-m+2=b…①-a2-ma-m+2=-b…②?

①+②: -2a2-2m+4=0,

∴a2=-m+2,

When m < 2, there are only two points m, n,

∴a=

2 meters.

At this time, the distance from m and n to y axis is 2m,

The coordinate of point C is (0,2-m), and S△MNC=27.

∴2× 12×(2-m)×2-m=27,

∴: The answer is m =-7.