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"Understanding quadratic equations of one variable" PPT courseware of quadratic equations of one variable
Question 1 A carpet surrounded by lace of equal width is as shown below. Its length is 8m and its width is 5m. If the area of the rectangular pattern in the center of the carpet is 18m2, how wide is the lace?
Solution: If the width of the lace is x m, then the length of the rectangular pattern in the center of the carpet is (8-2x) m and the width is (5-2x) m. According to the meaning of the question, the equation can be obtained:
(8-2x)(5 -2x) = 18.
After sorting, we get 2x²-13x+11=0
concept:
An integral equation that contains only one unknown and the highest degree of the unknown is 2 is called a quadratic equation.
Quadratic equations can usually be written in the following general form:
ax²+bx+c=0（a≠0)
Features: The left side of the equation is arranged according to the descending power of x, and the right side = 0
Judgment conditions:
(1) are all integral equations
(2) Contains only one unknown number
(3) The highest degree of unknown number is 2
The equation ax2 -2bx+a=2x2 about x, under what conditions is this equation a quadratic equation? Under what conditions is this equation a linear equation of one variable?
Solution: Shift: ax2 -2bx+a-2x2 =0
Combine similar items: (a-2)x2-2bx+a=0
Therefore, when a≠2, it is a quadratic equation;
When a=2, b≠0, it is a linear equation of one variable;
Variation exercise (1): (k+3)x|k|-1 -5x+6=0 is a quadratic equation of one variable with respect to x, then k=______.
Variation exercise (2): The constant term of the quadratic equation (m-1)x2 +5x+m2-1=0 about x is 0, then m=______.
Use the estimation method to find the approximate roots of a quadratic equation of one variable.
When solving some practical problems, the approximate value range can be determined according to the actual situation, so we can use the approximation method to find the approximate root.
1. The perimeter of a rectangle is 30 cm, the area is 54 cm, and the width is x cm.
(1) Make an equation according to the meaning of the question.
(2) Is x possible to be less than 0? Give reasons.
(3) Is it possible that x is greater than 15? Give reasons.
(4) Can you think of a way to find the length x of the rectangle?
Solution (1) Assume the width of the rectangle is x centimeters, then the length is (15-x) centimeters.
x(15 -x)=54
(2) x represents the actual width of the rectangle, which cannot be less than 0
(3) Impossible, because the sum of length and width is 15, x may be greater than 15.
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"Understanding quadratic equations of one variable" Quadratic equations PPT courseware 4:
"Understanding Quadratic Equations" Quadratic Equations PPT Courseware 4 1. Review Review For the quadratic equation (1) (8-2x) (5-2x)=18, that is: 2x2-13x+11=0; (2 )(x+6)2+72=102 That is: x2+12x-15=0. Can you find x in the equation separately? ..
"Understanding quadratic equations of one variable" Quadratic equations PPT courseware 3:
"Understanding Quadratic Equations" Quadratic Equations PPT Courseware 3 The length of the rectangular floor of the kindergarten activity classroom is 8 meters and the width is 5 meters. Now we are going to lay a carpet with an area of 18m2 in the middle of the floor. There will be no carpet around it. The width of the strip areas are all the same. Observe...
"Understanding quadratic equations of one variable" Quadratic equations PPT courseware 2:
"Understanding Quadratic Equations" Quadratic Equations PPT Courseware 2 Review and Thinking Can you make certain decisions based on the sales profits of goods? Like linear equations and fractional equations, quadratic equations are also an effective way to describe the real world. mathematical model. ..