It is known that the parabola y = MX & sup2; + (M-6) X-6 (the constant M is not equal to 0) (1) when m is the value, the distance between the two intersections of the parabola and the X axis is equal to 2 When I set up the equation, the answer is always wrong

It is known that the parabola y = MX & sup2; + (M-6) X-6 (the constant M is not equal to 0) (1) when m is the value, the distance between the two intersections of the parabola and the X axis is equal to 2 When I set up the equation, the answer is always wrong

Y = MX & sup2; + (M-6) X-6 = 0 and X-axis have two intersections (x1,0) (x2,0) X1 + x2 = (6-m) / mx1x2 = - 6 / m | x1-x2 \ ^ 2 = (x1 + x2) ^ 2-4x1x2 = 4 (6-m) 2 / M2 + 24 / M = 4m2-4m-12 = 0m1 = - 2, M2 = 6, and the discriminant (M-6) ^ 2 + 24m > 0 is substituted into M1 = - 2, M2 = 6 respectively

(1) when m is any real number, there is always an intersection between the parabola and the x-axis. (2) when the parabola and the x-axis intersect at two points a and B (A and B are on the left and right sides of the y-axis respectively), and OA ∶ ob = 2 &; 1, find the value of M

（1）△=m²-4(2m-4)
=m²-8m+16
=(m-4)²
Obviously (M-4) &# 178; ≥ 0
That is: △≥ 0
Therefore, no matter m is any real number, the parabola and X-axis always have intersection
(2) Let a (x1,0), B (x2,0)
Then: OA = - x1, OB = x2
Then: - X1: x2 = 2:1
Namely: X1 = - 2x2
Then: X1 + x2 = - X2, X1 * x2 = - 2x2 & # 178;
X1, X2 are the roots of the equation x & # 178; - MX + 2m-4 = 0
According to Weida's theorem: X1 + x2 = m, X1 * x2 = 2m-4
So:
-x2=m
-2x2²=2m-4
Substituting x2 = - m into formula 2, we get: - 2m & # 178; = 2m-4
2m²+2m-4=0
m²+m-2=0
(m+2)(m-1)=0
m1=-2,m2=1
When m = - 2, the equation x & # 178; - MX + 2m-4 = 0 is: X & # 178; + 2x-8 = 0, easy to get: X1 = - 4, X2 = 2, satisfying the meaning OA: OB = 2:1;
When m = 1, the equation x & # 178; - MX + 2m-4 = 0 is: X & # 178; - X-2 = 0, it is easy to get: X1 = - 1, X2 = 2, OA: OB = 1:2, rounding off;
So the value of M is - 2