1.y = x 2+(m-1) x+(m-2) and the x axis intersect at two points, a and b, so let a and b be the abscissa x 1, x2; The vertical coordinates are all 0, and there are:

AB=2, so |x 1-x2|=2.

X^2+(m- 1)x+(m-2)=0

According to the formula x1+x2 =-b/a =-(m-1) =1-m; x 1x2=c/a=m-2

|x 1-x2|^2=2^2=4

| x1-x2 | 2 = (x1-x2) 2 = (x1+x2) 2-4x1x2 = (1-m) 2 No.4.

( 1-m)^2 - 4(m-2)=4

1-2m+m^2-4m+8=4

m^2-6m+5=0

(m- 1)(m-5)=0

M= 1 or 5

2.Y=X^2-(m-3)x-m

Two intersection points δ > 0 (m-3) 2+4m >: 0; m^2-2m+9>； 0; m^2-2m+ 1+8>； 0; (m- 1)^2+8>； Any value of 0, m is valid.

The two intersections with the X axis are on the left side of the Y axis, so both X 1 and X2 are less than 0. The relationship between the combined heel and the coefficient is expressed as:

x 1+x2 & lt； 0, (at least one of them is negative) x 1+x2 =-b/a = m-3.

x 1x 2 & gt； 0 (two identical numbers) x1x 2 = c/a =-m > 0m & lt； 0

Therefore, δ > 0, x 1+x2 is satisfied.

Solution: m