"Solving Quadratic Equations of One Variable" PPT Courseware 3 of Quadratic Equations of One Variable

Description

"Solving Quadratic Equations of One Variable" PPT Courseware 3 of Quadratic Equations of One Variable

Question 1

A bucket of a certain paint can cover an area of ​​1500dm2. Li Lin used this bucket of paint to paint all the outer surfaces of 10 boxes with the same cube shape. Can you calculate the edge length of the box?

Solution: Suppose the edge length of the cube is x dm, then the surface area of ​​a cube is 6x2dm2. Based on the area that can be painted with a bucket of paint, the equation is listed

10×6x2=1500

From this we get x²=25

According to the meaning of square roots, we get: x1=5, x2=-5

It can be verified that 5 and -5 are the two roots of the equation, but the edge length cannot be a negative value, so the edge length of the cube is 5dm.

practice

1. Fill in:

(1) The roots of the equation x²=0.25 are x1=0.5, x2=-0.5.

(2) The roots of the equation 2x²=18 are x1=3, x2=-3.

(3) The roots of equation (2x-1)²=9 are x1=2, x2=-1.

2. Choose an appropriate method to solve the following equations:

(1)x2-81＝0 (2)2x2＝50 (3)(x＋1)2=4

Class summary

What did we learn in this lesson? So how to use the square root method to solve a quadratic equation of one variable?

There are three steps to solve a quadratic equation of one variable using the square root method:

The first step: transform the original equation into the form x²=p or (mx+n)²=p (p≥0);

Step 2: Take the square root and convert the quadratic equation into a linear equation, that is, reduce the quadratic equation to a linear equation.

Step 3: Solve the linear equation of one variable and find the roots of the equation.

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Update Time: 2024-10-17

This template belongs to Mathematics courseware People's Education Press Ninth Grade Mathematics Volume 1 industry PPT template

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