1, direct Kaiping method; 2. Matching method; 3. Formula method; 4. Factorial decomposition method.
1, direct Kaiping method:
The direct Kaiping method is a method to solve a quadratic equation with a direct square root. Solve the shape such as (x-m) 2 by direct Kaiping method; =n
(n≥0)
An equation whose solution is x = √ n+m.
.
2. Matching method: use matching method to solve the equation AX 2+BX+C = 0.
(a≠0)
First, move the constant c to the right of the equation: ax 2+bx =-c.
Convert the quadratic term into1:x 2+b/ax =-
c/a
Add half the square of the coefficient of the first term on both sides of the equation: x 2+b/ax+ (
b/2a)^2=-
c/a+(
b/2a)^2；
The left side of the equation becomes a completely flat road: (x+b/2a.
)2=
-c/a﹢﹙b/2a﹚？
When b? When -4ac≥0, x+b/2a
= √﹙﹣c/a﹚﹢﹙b/2a﹚？
∴x=﹛﹣b [√﹙b？ -4ac]-/2a (this is the root formula)
3. Formula method: convert the quadratic equation of one variable into a general form, and then calculate the discriminant △=b? The value of -4ac, when b? -4ac≥0, coefficient a,
b，
The value of c is substituted into the root formula x = [-b √ (b? -4ac)]/(2a)
,
(b？ -4ac≥0), the root of the equation can be found. 4. Factorial decomposition method: the quadratic trinomial on one side of the equation is decomposed into the product of two linear factors, so that the two linear factors are equal to zero respectively, and two linear equations are obtained. The roots obtained by solving these two linear equations are the two roots of the original equation. This method of solving a quadratic equation with one variable is called factorization. Usually, factorization is the most commonly used method to solve quadratic equations with one variable. When factorization is applied, the equation is written in a general form and the quadratic coefficient is turned into a positive number.
Direct leveling method is the most basic method.
Formula and collocation are the most important methods. Formula method is suitable for any quadratic equation with one variable (some people call it universal method). When using the formula method, the original equation must be transformed into a general form to determine the coefficient, and before using the formula, the value of the discriminant should be calculated to judge whether the equation has a solution.
Matching method is a tool to derive formulas. After mastering the formula method, you can directly use the formula method to solve the quadratic equation of one variable, and generally do not need to use the matching method.
Solve a quadratic equation with one variable. However, collocation method is widely used in the study of other mathematical knowledge, and it is one of the three important mathematical methods required to be mastered in junior high school, so we must master it well. Three important mathematical methods: method of substitution, collocation method and undetermined coefficient method.