Cross multiplication solves a quadratic equation

Cross multiplication method to solve a quadratic equation: The method of cross multiplication is simply as follows: the left side of the cross is multiplied equals the quadratic term, the right side multiplies is equal to the constant term, and the cross multiplication and addition are equal to the primary term.

It should be noted that cross multiplication is essentially a form of simplified equation that can factor quadratic trinomials, but it is important to pay attention to the symbols of the coefficients.

The method of cross multiplication: the left side of the cross is multiplied equals the quadratic term coefficient, the right side multiplied is equal to the constant term, and the cross multiplication and then added is equal to the primary term coefficient. Usefulness of Cross Multiplication: Use cross multiplication to break down factors. Cross multiplication is used to solve a quadratic equation.

Advantages of cross multiplication: The speed of solving problems with cross multiplication is relatively fast, which can save time, and the amount of calculation is not large, and it is not easy to make mistakes. Defects of cross multiplication:

Some problems are easier to solve using cross multiplication, but not every problem is easy to solve using cross multiplication. Cross multiplication is only available for quadratic trinomial type problems. Cross multiplication is more difficult to learn.

The cross multiplication method to solve a quadratic equation should be divided into the product of two factors, and the constant term should be divided into the product of two constants, and then the cross pattern should be cross-multiplied. If the result of the merge is not a one-time item, you need to readjust the attempt.

Cross-cross factoring: first split the quadratic term coefficient into two products, then the constant term into two products, and then cross the product to equal the primary term coefficient.

1. Extracting the common factor method.

2. Formula method (squared difference formula and perfect squared formula).

For example: matching method and cross method, etc.

x+2y)(2x-11y)=2x2-7xy-22y2。

x-3)(2x+1)=2x2-5x-3。

2y-3)(-11y+1)=-22y2+35y-3。

This is known as double cross multiplication.

Method mantra of cross multiplication:

The left side of the cross is multiplied equally, the right side is multiplied equals the constant term, and the cross multiplication is added to the primary term coefficient.

Usefulness of cross multiplication:

1) Use cross multiplication to break down the factor.

2) Use cross multiplication to solve a quadratic equation.

Advantages of Cross Multiplication:

Using cross multiplication to solve problems is relatively fast, can save time, and the use of arithmetic is not large, and it is not easy to make mistakes.

The cross multiplication method is a kind of solution square rolling hole method used in the old cracking of the unary quadratic equation, which is based on whether the quadratic coefficient and the constant term can be split into the product of four numbers to solve the equation, as shown in the following figure.

The cross multiplication method is to use the cross multiplication method to convert the unary quadratic equation into the form of (ax+b)(cx+d)=0, and then convert ax+b=0 or cx+d=0 to obtain x=-b a, x=-d c