"Solving quadratic equations of one variable using formula method" PPT courseware 2

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"Solving quadratic equations of one variable using formula method" PPT courseware 2

1. Use the combination method to solve the following equations

2x²-12x+5=0

2. What are the steps to solve quadratic equations of one variable using formulas?

1. If the coefficient of the quadratic term is not 1, change the coefficient of the quadratic term to 1 (divide both sides of the equation by the coefficient of the quadratic term);

2. Move the constant term to the right side of the equation;

3. Add half the square of the absolute value of the linear coefficient to both sides of the equation, so that the left side becomes a perfect square;

4. If the right side of the equation is a non-negative number after sorting, use the direct square root method to solve it. If the right side is a negative number, it means that the original equation has no real roots.

Can you solve the equation ax²+bx+c=0(a≠0) using the matching method?

1. Change to 1: Change the coefficient of the quadratic term to 1;

2. Move the term: Move the constant term to the right side of the equation;

3. Recipe: Add half the square of the absolute value of the coefficient of the linear term to both sides of the equation;

4. Deformation: factorize the left side of the equation and combine similar factors on the right side;

5. Square root: According to the meaning of square root, the square root of both sides of the equation;

6. Solve: Solve linear equations of one variable;

7. Definite solution: Write the solution of the original equation.

Example 1. Use the formula method to solve the equation 5x²-4x-12=0

1. Deformation: transform known equations into general forms;

2. Determine the coefficients: write the coefficients in terms of a, b, c;

3. Calculate: the value of b²-4ac;

4. Substitution: Substitute the relevant values ​​into the formula for calculation;

5. Definite roots: Write the roots of the original equation.

General steps for solving quadratic equations of one variable using the formula method:

1. Put the equation into a general form and write the values ​​of a, b, and c.

2. Find the value of b²-4ac.

3. Substitute the root formula: X=-b±√b²-4ac (a≠0, b²-4ac≥0)

4. Write the solution to the equation: x1=? x2=?

practise:

Solve the following equations using the formula method:

1. x² +2x =5

2. 6t² -5 =13t

Thought questions:

1. The quadratic equation of x with respect to x is ax²+bx+c=0 (a≠0). When a, b, c satisfy what conditions, the two roots of the equation are opposite to each other?

2. When m takes any value, the equation x²+(2m+1)x+m²-4=0 has two equal real number solutions.

Think about it:

Regarding the quadratic equation ax²+bx+c=0(a≠0), when a, b, and c satisfy what conditions, the two roots of the equation are opposites of each other?

summary

The key to using the formula method to solve quadratic equations of one variable is the problem-solving steps:

1. First write a, b, c

2. Then find b²-4ac

3.Finally substitute the formula

When b²-4ac≥0, there are two real roots

When b²-4ac<0, the equation has no real solution

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For more information about the PPT courseware "Using the Formula Method to Solve Quadratic Equations of One Dimension", please click the "Using the Formula Method to Solve Quadratic Equations of One Dimension" ppt tag.

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"Solving quadratic equations of one variable using the formula method" PPT courseware for quadratic equations of one variable Review and review 1. Use the formula method to solve the following equation 2x-12x+10=0 2. What are the steps to use the formula to solve the quadratic equation of one variable? 1. Change to 1: Change the coefficient of the quadratic term to 1 (divide both sides of the equation by...

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Update Time: 2024-11-21

This template belongs to Mathematics courseware Qingdao Edition Ninth Grade Mathematics Volume 1 industry PPT template

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