The real coefficient equation f (x) = x ^ 2 + ax + 2B = 0 has one root in (0,1) and the other root in (1,2) The range of (b-2) / (A-1)

The real coefficient equation f (x) = x ^ 2 + ax + 2B = 0 has one root in (0,1) and the other root in (1,2) The range of (b-2) / (A-1)

F (0) = 2B, f (1) = 1 + A + 2B, f (2) = 4 + 2A + 2B, the opening of quadratic function image is upward, so 2b is greater than 0, 1 + A + 2b is less than 0, 4 + 2A + 2b is greater than 0, and then use linear programming to draw the image. What you seek can be seen as the slope range from (a, b) to (1,2) points in the surrounding area, I believe you can do it

The real coefficient equation f (x) = x2 + ax + 2B = 0 has one root in (0,1) and the other root in (1,2). Find: (1) the range of B − 2A − 1; (2) the range of (A-1) 2 + (b-2) 2; (3) the range of a + B-3

If we know that f (0) > 0f (1) < 0f (2) > 0, then its constraint condition is: b > 01 + A + 2B < 02 + A + b > 0. Its feasible region is a triangle composed of a (- 3,1), B (- 2,0) and C (- 1,0)

One root of the real coefficient equation x * x + ax + 2B = 0 is in (0,1), and the other root is in (1,2)?
x^2+ax+2b

Let f (x) = x & # 178; + ax + 2B
Because one root is in (0,1), the other root is in (1,2)
So f (0) = 2B > 0
f(1)=1+a+2b＜0
f(2)=4+2a+2b＞0
B > 0
1+a+2b＜0
2+a+b＞0
Draw the feasible region in the coordinate axis a0b
The geometric meaning of B / A is the slope from point (a, b) to point (0,0)
From the feasible region, when (a, b) is the intersection of 1 + A + 2B = 0 and 2 + A + B = 0, the slope is the smallest
And the intersection point is (- 3,1)
So B / a = (1-0) / (- 3-0) = - 1 / 3
Answer: the minimum value is - 1 / 3

Solving a problem of binary linear equations
It is known that the two solutions of the equation AX + BX = - 1 are x = - 2, y = - 1 and x = 4, y = 3

Taking the values of X and Y into the original equations, we get - 2a-b = - 1, 4A + 3B = - 1
The solution is a = 2, B = - 3

Help me solve a system of linear equations with two variables~
{3x+4y=22.3
Solve the equation {4x + 5Y = 28.5

4X + 5y-3x + 4Y = 6.2 (i.e. x + y = 6.2) 3x + 4y-3x-3y = y = 3.7 x = 2.5 y = 3.7

A solution to a system of linear equations of two variables
Solving the equations 21x + 37y = 327
37x+21y=311

21x+37y=327 ..1
37x+21y=311 ..2
2-1
16x-16y=-16
About 16 percent
x-y=-1
y=6 x=5

Finding the solution of a system of linear equations of two variables
x+y+(4-x-y)=4
{
3x+(6-x-y)=6

I'll tell you exactly
There is no solution to this problem
Because the first formula is reduced to 0 = 0
So the first formula is useless
According to the binary equation, at least two sets of equations are needed to have solutions
There is no solution to the equations
It can only be obtained from the second formula: 2x-y = 0

Solving a system of linear equations of two variables
x+2y+x=180
y+30+x+2y=180

From equation 1, we can get 2 (x + y) = 180 and X + y = 90
Equation 2 can be reduced to (x + y) + 2Y + 30 = 180
If x + y = 90 is replaced by near equation 2, then 90 + 2Y + 30 = 180
Y = 30
x=90-30=60

The common solution of binary linear equations
The first equation is 2x + 5Y + 6 = 0
ax-by+4=0
The second equation 3x-5y = 16
bx+ay=-8
Find the value of (2a + b) to the power of 2007

Because the solutions are the same, we find the common solution of the first set of equations 2x + 5Y + 6 = 0 and the second set of equations 3x-5y = 16
The solution is x = 2, y = - 2
Substituting x = 2, y = - 2 into the other two equations, that is, the solution 2A + 2B + 4 = 0, 2b-2a = - 8, the solution a = 1, B = - 3
So (2a + b) ^ 2007 = - 1

How to understand the common solution in the definition of solution of binary linear equations

You see, binary linear equation (not system) x + y = 2. You see, any value of X and y can be taken, as long as their sum is equal to 2. So it is not a common solution. What is a common solution? Only binary linear equation system has a common solution. For example, x + y = 2
2x-y=3
These two equations are combined with each other and restrict each other. That is to say, to satisfy these two equations, there is only one answer. It's not to take whatever value you want. If you don't understand, ask me again!