The formula method solves the one dimensional quadratic equation, and the formula method how to solv

1 The concept of a quadratic equation includes three conditions: (1) an integral equation; (2) there is only one unknown in the equation; (3) The highest number of unknowns is 2".

The concept of a quadratic equation "contains only one unknown, and the highest number of unknowns is 2" is for the general form of the equation For example, is the equation 2x 2 2x 1 2x 2 a quadratic equation? The equation should be sorted out first to get 2x 1 0, so this equation is not a quadratic equation

2 When finding quadratic terms, primary terms, and constant terms, it is necessary to first sort out the equations, turn the equations into a general form, i.e., ax 2 bx c 0, and then determine the equation ax 2 bx c 0 is a unary quadratic equation only when a≠0, for example, when a0, b≠0, it is a unary quadratic equation, so if it is clearly pointed out that ax2 bx c 0 is a unary quadratic equation, then the condition a≠0 must be included

3 The direct open-leveling method is suitable for solving equations in the form of x 2 a, when a 0, the equation has a real solution; When a 0, the equation has no real solution

4. The matching method is to first move the constant term of the equation to the right side of the equation, and then match the left side to a perfect flat method, if the right side is a non-negative number, you can further find its solution by the direct open flat method; If the right side is negative, there is no real solution to the equation

5 The root finding formula is for the general form of a one-dimensional quadratic equation, when using the root finding formula, the equation must be transformed into a general form in order to correctly determine the coefficients, before applying the formula, the value of b 2 4ac is calculated, and when b 2 4ac is 0, the root of the equation is obtained by substituting the formula; When b 2 4ac 0, the equation does not have a real root, so there is no need to substitute the formula

Example: Use the formula method to solve the following equations:

1)2x^2＋7x＝4；(2)x^2－1＝2 x．

Solution: (1) The equation can be deformed into 2x 2 7x 4 0

a＝2，b＝7，c＝－4，b2－4ac＝72－4×2×(－4)＝81＞0，x＝ ．x1＝ ，x2＝－4．

2) The equation can be deformed into x 2 2 x 1 0

a＝1，b＝－2 ，c＝－1，b2－4ac＝(－2 )2－4×1×(－1)＝16＞0．

x＝ ．x1＝ ＋2，x2＝ －2．

Note: When using the formula method to solve an equation, it is necessary to first convert the equation into a general form

1.The equation is the general formula ax 2 + bx + c = 0:2

Determine the discriminant formula and calculate the δ (delta, i.e., b 2-4ac); 3.If 0 is δ>, the equation has two unequal real roots in the field of real numbers: ; If δ=0, the equation has two equal real roots in the real number field:

If δ< 0, the equation has no solution in the field of real numbers (abbreviation"There are no solid roots"), but within the imaginary number field, it is solved as x=[-b (4ac-b 2)i] 2a.

The basic form of the equation is a*x 2+b*x+c=0, and the three constant terms a, b, and c are arbitrary numbers. =b 2-4*a*c, first judge the case of the root according to the size of : if >0, the equation has two unequal real roots, and if =0, the equation has two equal real roots (two equal is one, but you don't have to say two equal.

0, there is no real root. (You definitely didn't learn imaginary numbers, so leave it alone).

If the equation has roots, the root is x=(-b (2*a).

For example, a quadratic equation: ax +bx+c=0.

The formula method can be obtained:

x=[-b±√(b²-4ac)]/2a）

This gives you two x values.

Solve the positive equation of socks disadvantages (k 2-1) x 2-6 (3k-1) x + 72 = 0, and use the cross phase divination branch multiplication to decompose the left side of the equation due to repentance [(k+1)x-12][(k-1)x-6]=0

The solution results in x=12 (k+1), y=6 (k-1)x, and y are all positive integers k=2 or 3

First of all, the number of roots is determined by b -4ac, and b -4ac 0 means that the equation has two unequal real roots.

b -4ac 0 indicates that the equation has no real roots, and b -4ac = 0 indicates that the equation has two equal real roots.

The algebraic calculator in the Yili Zhishi software was used on the mobile phone to solve, and the result was as follows:

The process is as follows: