A problem of quadratic equation of one variable If 0 is the solution of the equation (m-2) x & sup2; + 3x + M & sup2; + 2m-8 = 0 about X, find the value of real number m and discuss the solution of this equation

A problem of quadratic equation of one variable If 0 is the solution of the equation (m-2) x & sup2; + 3x + M & sup2; + 2m-8 = 0 about X, find the value of real number m and discuss the solution of this equation

If 0 is brought in, we can get m + 2m-8 = 0
M = - 4 or 2
So let's bring m in
-6X + 3x = 0
Or 3x = 0
When m = - 4, the solution is x = 0 or x = 1 / 2
When m = 2, the solution is x = 0
Note: if the title statement is a quadratic equation with one variable, then M = 2 should be omitted, because the quadratic term of quadratic equation with one variable is not 0

A problem of quadratic equation of one variable
It is known that: X & sup2; + PX + q = 0, when P & sup2; - 4q ≥ 0, x = - P ± root P & sup2; - 4q / 2
(1) Denote X1 + X2, x1x2 with P and Q
(2) If two of the equations X & sup2; - 3x-2009 = 0 are X1 and X2, please use the conclusion of (1) and the concept of the root of the equation to calculate the value of X1 & sup2; - 2x1 + x2

（1）X1+X2=-p X1X2=q
（2）X1²-2X1+X2=(X1²-3X1)+(X1+X2)=2009+3=2012