If there are two unequal real roots of the quadratic equation x - (M + 1) x-m = 0 with respect to x, find the value range of M. 4. Given the set a = {x | x-16 ＜ 0}, B = {x | x-4x + 3 ＞ 0}, find a ∪ B

If there are two unequal real roots of the quadratic equation x - (M + 1) x-m = 0 with respect to x, find the value range of M. 4. Given the set a = {x | x-16 ＜ 0}, B = {x | x-4x + 3 ＞ 0}, find a ∪ B

If the equation x ^ 2-2 (1-m) x + m ^ 2 = 0 has two real roots α, β
If the equation x ^ 2-2 (1-m) x + m ^ 2 = 0 has two real roots α, β, then the value range of α + β is

α+β=1-m
△=B^2-4AC>=0
That is 4 (1-m) ^ 2-4m ^ 2 > = 0
-8m+4>=0
m=1.5

Given that the two roots of the equation x ^ 2 + 2mx-m + 12 = 0 are greater than 2, then the value range of the real number m
Given that the two roots of the equation x ^ 2 + 2mx-m + 12 = 0 are greater than 2, then the value range of the real number m

Let two roots be X1 and X2, then X1 + x2 = - 2m > 4, X1 * x2 = 12-m > 4. In this way, the range of M can be obtained by combining two inequalities. In addition, the equation must have two roots, so ⊿ > = 0 should be satisfied. In this way, the range of M can be obtained by synthesizing the above results