(1) According to the equation, there are two unequal real roots, and the value range of m can be found from the definition of the quadratic equation of one variable and the discriminant of the roots;
(2) First, find the value of a positive integer m, so as to determine the analytical expression of the quadratic function and get the coordinates of the intersection of the analytical expression and the X axis. From the image, we can know that the straight line y=kx+3 passes through point A and point B, and then the value of k can be obtained.
Answer:
Solution: (1) △ = (4-m) 2-12 (1-m) = (m+2) 2,
From the meaning of the question, (m+2) 2 > 0 and 1-m ≠ 0.
Therefore, the value range of m satisfying the meaning of the question is all real numbers of m≦-2, m≠ 1.
(2)∵ positive integer m satisfies 8-2m > 2,
The acceptable values of ∴m are 1 and 2.
Quadratic function y = (1-m) x 2+(4-m) x 3,
∴m=2.
The quadratic function is y =-x 2+2x+3.
∴ The coordinates of point A and point B are (-1 0) and (3,0) respectively.
The image folded according to the meaning of the question is shown in the figure.
According to the image, the straight line y=kx+3 passes through point A and point B. 。
It can be found that the value of k at this time is 3 or-1 respectively.