1. Let m and n be positive integers, and M is not equal to 2. If for all real numbers T, the distance between the image of quadratic function y = x + (3 + MT) x-3mt and the two intersections of X axis is not less than | 2T + n | to find the value of m and n 2. It is known that M is a positive integer. If the roots of the equation x cube + (a + 17) x square + (38-a) x-56 = 0 about X are all integers, find the value of a and the integer root of the equation

1. Let m and n be positive integers, and M is not equal to 2. If for all real numbers T, the distance between the image of quadratic function y = x + (3 + MT) x-3mt and the two intersections of X axis is not less than | 2T + n | to find the value of m and n 2. It is known that M is a positive integer. If the roots of the equation x cube + (a + 17) x square + (38-a) x-56 = 0 about X are all integers, find the value of a and the integer root of the equation

1. For the function whose quadratic term is 1, the distance | x1-x2 | from the intersection of x-axis is
√ (x1-x2) 2 = √ △ (it should be able to work out)
So it can be expressed
If △≥ | 2T + n |, the two sides are squared, and △ can be obtained by substituting it into the knowledge of inequality (or the knowledge of quadratic function image), I will not calculate the details
2. First, the three root products are - 56 and all integers, and the decomposition is 56 = 2 * 2 * 2 * 7
At the same time and = - (a + 17), smaller than - 17, so there must be two cases
-1-2-28 can be, and a = 14 can be substituted into the original equation to know that these are not its solutions
-1-4-14 can be, and a = 2 can be substituted into the original equation to know that these are not its solutions
In the same way - 1 - 1 - 56 / 1 1 - 56 and other situations are ignored
You should be able to work it out in this way
There are many symbols I can't type, but I hope my answer can help you