Finding the number of zeros of a function ①-x^2-3x-2 x≤0 g(x)=f(x)+x={ ②x-2 x>0 Step by step I'm not very good at it { ①-x^2-3x-2 x≤0 g(x)=f(x)+x={ { ②x-2 x>0

You can count that
x> Let X-2 = 0, x = 2 hold
When x ≤ 0, let - X & sup2; - 3x-2 = 0, (x + 1) (x + 2) = 0, X1 = - 1, X2 = - 2, hold, two,
There are three in all

The number of zeros of cubic function
How to judge? Some can be decomposed into a fractional function and a quadratic function, draw a picture to find the intersection point, several intersections are several zeros. Some can be decomposed into factors. But how to quickly find out the method? Can only two methods be tried one by one?

Finally, the corresponding function values of negative infinity, maximum, minimum and positive infinity are found in the original equation. If the product of two adjacent function values is greater than zero, there will be no zero in the region between them, otherwise there will be zero

Exercise and process of approximate solution of equation by dichotomy

The basic principle of dichotomy is the zero point theorem of continuous function
Let f (x) be continuous on a closed interval [a, b], and f (a) and f (b) have different signs (i.e. f (a) × f (b))

It is necessary to find the approximate solution of the equation by dichotomy-
Approximate value of positive root of equation x ^ 2-2x-2 = 0 by dichotomy (accurate to 0.1)

First of all, you are a quadratic equation of two variables. You can know that there are two solutions by using the formula. Then, because the parabola has two monotone intervals, you have to discuss it twice. The lowest point of the function can be obtained from the equation is 1, and the value can be obtained by substituting it into - 3. Take this as the boundary, and then substituting it into 0, the value can be obtained as - 2, indicating that the positive root is on the right. Then you take 2, the value can be obtained as - 2, and the value can be obtained as 1 by taking 3, Explain that there are zeros in 2 to 3, then divide the sum of them by 2.5 to get the value less than 0, and then narrow the interval to 2.5 to 3, and then narrow the range all the time in the same way until the subtraction of the left and right numbers is less than or equal to 0.1

Approximate solution of equation by dichotomy
If the function y = 2 ^ 2x + 2 ^ x * a + A + 1 has zero, find the value range of real number a
I hope there is a process. Let's say the function is 2x times of 2 + x times of 2 multiplied by a + A + 1

Let z = 2 ^ x, then the equation of degree y = Z ^ 2 + AZ + A + 1 (z > 0) has positive roots if delta = a ^ 2-4 (a + 1) > = 0 (- A + sqrt (delta)) / 2 > 0, so delta = a ^ 2-4 (a + 1) > = 0A ^ 2-4a + 4 > = 8 (A-2) ^ 2 > = 8A > = 2sqrt (2) + 2 or a0sqrt ((A-2) ^ 2-8) > AAA ^ 2 and a > 0} a

Seeking approximate solution of equation by dichotomy in senior one mathematics
If the odd function f (x) = x ^ 3 + BX ^ 2 + CX's three zeros x1, X2, X3 satisfy x1x2 + x2x3 + x1x3 = - 2, then B + C=_______ .
Write the detailed process

f(x)=x^3+bx^2+cx
x³+bx²++cx=x(x²+bx+c)=0
When there is a zero point, x = 0
The other two zeros satisfy X & sup2; + BX + C = 0
X1x2 + x2x3 + x1x3 = - 2 because of complete symmetry, arbitrarily set X1 = 0
So x2x3 = - 2
x2x3=c
c=-2
f（x）=x³+bx²-2x
Odd function f (x) = - f (- x)
∴b=0
b+c=-2

How to judge the approximate range when seeking the approximate solution of equation by dichotomy
Is it necessary to judge the general range by drawing an image?

Suppose f (x) is continuous on the interval (x, y)
First, find that a and B belong to the interval (x, y), so that f (a) and f (b) are different,
It is shown that there must be a zero point in the interval (a, b), and then find f [(a + b) / 2],
Now suppose f (a) 0, A0, then there are zeros in the interval (a, (a + b) / 2), (a + b) / 2)

Roots of mathematical equations and zeros of functions in grade one of senior high school
1. If f (x) = (x-1) / x, then the zero point of F (x) = f (4x) - x is
2. If the function f (x) = ax + 2A + 1 has and has only one zero point in the interval [- 1,1], then the value range of real number a is
3. The zero point of the function y = f (x) is the equation______ The root of
The master~~

F (x) = (4x-1) / 4x-x = 1-1 / 4x-x, so its 0 point is: (0.5,0)
2.f(-1)xf(1)

I went to high school on the concept of function. I don't know much about the concept of function in grade one
Let a and B be nonempty sets of numbers
A certain corresponding relation F, such that for the
Any number x is uniquely determined in the set B
If f (x) corresponds to it, then it is called
A function from set a to set B,
F: how to understand it in Chinese
What is a function? It's the definition of a function. Then what is a function? Can we use the function as How to tell me thank you

It means to take any number from the set a
There is always a number in B corresponding to it, and there is only one!
And F is the corresponding rule!
This is the function
For example:
A is r
B is a nonnegative number
F can take square function, but not square function
Because there are many elements in a that can't open a square at all, so naturally there are no corresponding elements in B
And square, because the square is equal to or greater than 0, so no matter which number it is, it has a square, so it can be a function

Some conceptual understanding of high school function
1. What is the range? How to understand it? The definition field is to make the function meaningful, so the range is only a set generated by a set under the corresponding rule? Why is the definition field of quadratic function R, and there are two cases of the range?
2. To judge the same function is to define the range. The range and the corresponding rule are the same. How to understand the range and the corresponding rule`

Read more about concepts. You may not understand them for the time being, but you will understand them after a long time

Finding the number of zeros of a function ①-x^2-3x-2 x≤0 g(x)=f(x)+x={ ②x-2 x>0 Step by step I'm not very good at it { ①-x^2-3x-2 x≤0 g(x)=f(x)+x={ { ②x-2 x>0