People's Education Press Ninth Grade Mathematics Volume 1

Description

"Quadratic Equation of One Variable" PPT Courseware 3

Early knowledge of content:

1. Equation: An equation containing unknown numbers is called an equation.

2. Solution of the equation: The value of the unknown that makes the left and right sides of the equation equal is called the solution of the equation.

3. Roots of equations: The solution of a one-variable equation is also called the root of the equation.

4. A linear equation of one variable: an integral equation that contains an unknown number and the highest degree of the unknown number is 1.

5. Quadratic equation: an integral equation containing two unknowns, and the highest degree of the unknown terms is 1

6. Fractional equations: equations containing unknown numbers in the denominator

7. Radical equations: equations containing unknown numbers under the radical sign

8. Quadratic equation of one variable: an integral equation that contains an unknown number and the highest degree of the unknown number is 2.

9. The general form of a quadratic equation: ax2+bx+c=0 (a≠0, a, b, c are constants)

The concept of quadratic equation of one variable

An integral equation that contains only one unknown (univariate) and the highest degree of the unknown is 2 (quadratic) is called a quadratic equation of one variable.

Instructions and advice

To judge whether an equation is a quadratic equation, you cannot just look at the surface. You must first simplify it if it can be simplified, and then check whether the highest degree of the unknowns of the equation is 2.

In the general form of a quadratic equation of one variable, there are at most three terms on the left side of "=". The linear terms and constant terms may not appear, but the quadratic terms must exist, and the left side is usually arranged according to the descending power of x: special attention is paid to "＝ "The right side of " must be sorted to 0.

Quadratic equation of one variable: a≠0

General form: The right side of "=" must be 0

Expand and improve

1. It is known that one root of the equation x2+mx-12=0 is x=-2, find the value of m. m=-4

2. The solution of equation (x-1)(x+3)(x-2)=0 is x1=1,x2=-3,x3=2

3. It is known that m is a root of the equation x2+x-2014=0, and the value of m2+m is 2014.

Quadratic equation of one variable: ax2+bx+c=0,

If a+b+c=0, then the equation: ax2+bx+c=0, there must be a root equal to 1

If a-b+c=0, then the equation: ax2+bx+c=0, there must be a root of -1

If 4a+2b+c=0, then the equation: ax2+bx+c=0, there must be a root of 2

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For more information about the PPT courseware "Quadratic Equation of One Variable Equation", please click the "Quadratic Equation of One Variable Equation" ppt tab.

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Update Time: 2024-09-30

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