Distribution of roots of quadratic equation Find the value range of the real number m so that the two α and β of the equation x ^ 2 + 2 (m-1) x + 2m + 6 = 0 satisfy the following conditions: (1) , are greater than 1 (2) One less than 2, one more than 2 (3) , 0

Distribution of roots of quadratic equation Find the value range of the real number m so that the two α and β of the equation x ^ 2 + 2 (m-1) x + 2m + 6 = 0 satisfy the following conditions: (1) , are greater than 1 (2) One less than 2, one more than 2 (3) , 0

1. M-1 > 1 (the axis of symmetry is on the right side of x = 1)
4m + 5 > 0 (when x = 1, y = x ^ 2 + 2 (m-1) x + 2m + 6 > 0)
m^2-4m-11>0（b^2-4ac>0）
Three equations can be solved in the common interval
2.6m+6

In image translation, the vector is used to represent the amount of translation. The upper and lower numbers represent the translation in which direction respectively
Emergency

Take (a, b) as an example
A is the translation in the x-axis direction, a is shifted to the right and a is shifted to the left
B is the translation in the y-axis direction, B is positive up and negative down

In the complex plane, rotate the vector corresponding to the complex number 2-radical 5I by 2 / 2 in the counter clockwise direction. What is the modulus of the complex number corresponding to the obtained vector

No matter how many degrees of rotation, the length of the vector remains unchanged, so the module is the original, that is, 4 + 5 equals 3 under the root sign