"Inequality" Equality and Inequality PPT (Solution of Quadratic Inequality of One Variable in Lesson 3)

"Inequality" Equality and Inequality PPT (Solution of Quadratic Inequality of One Variable in Lesson 3)

Part One: Learning Objectives

Be able to solve quadratic inequalities of one variable with the help of factorization or combination methods

Will convert simple fractional inequalities into quadratic inequalities of one variable to solve

Inequality PPT, part 2 content: independent learning

Problem guide

Preview the contents of textbook P68-P71 and think about the following questions:

1. What is the definition of quadratic inequality of one variable?

2. How to solve quadratic inequalities of one variable using factorization?

3． How to solve quadratic inequalities of one variable using the matching method?

A preliminary exploration of new knowledge

1. The concept of quadratic inequality of one variable

Generally, inequalities of the form _______________ are called quadratic inequalities of one variable, where a, b, c are constants, and a≠0.

■Instructions from famous teachers

The inequality signs in quadratic inequalities of one variable can also be "<", "≥", "≤", etc., that is, ax2+bx+c<0(a≠0), ax2+bx+c≥0(a≠0), ax2+bx+c≤0(a≠0) are all Quadratic inequality of one variable.

2. Solve quadratic inequalities of one variable using factorization method

Generally, if x10 is_______________________________.

3． Solve quadratic inequalities of one variable using the matching method

The quadratic inequality ax2+bx+c>0(a≠0) of one variable can always be changed into the form of _______________ or _______________ through formula, and then based on the knowledge of the positive and negative of k, the solution set of the original inequality can be obtained.

self-test

Judge whether it is true or false (mark “√” if it is correct and “×” if it is wrong)

(1)mx2－5x+2<0 is a quadratic inequality of one variable. ()

(2)5x2－mx+2<0 is a quadratic inequality of one variable. ()

(3) The solution set of inequality (x-1)(x-2)>0 is (1, 2). ()

The solution set of inequality-2x2+x+3<0 is ()

A.{x|x<－1}B.xx>32

C.x－132

If the set A={x|-1≤2x+1≤3}, B=x|x-2x≤0, then A∩B=()

A． {x|-1≤x<0} B. {x|0

C. {x|0≤x≤2} D． {x|0≤x≤1}

Inequality PPT, the third part: interactive teaching and practice

Solve quadratic inequalities of one variable without parameters

Solve the following inequalities:

(1)2x2+7x+3>0;

(2)-4x2+18x-814≥0;

(3)-2x2+3x-2<0;

(4)-12x2+3x-5>0.

regular method

Methods for solving quadratic inequalities of one variable without parameters

(1) If the quadratic equation corresponding to the inequality can be factorized, that is, it can be transformed into the product form of several algebraic expressions, then the solution set of the inequality can be obtained directly from the roots of the quadratic equation and the direction of the inequality sign.

(2) If the quadratic equation corresponding to the inequality can be transformed into a completely square form, no matter what value it takes, the perfect square form is always greater than or equal to zero, then the solution set of the inequality is easy to obtain.

(3) If neither of the above two methods can solve the problem, the general method of finding the solution set of quadratic inequalities of one variable, that is, the discriminant method, should be used.

Solving Quadratic Inequalities of One Variable with Parameters

Solve the inequality ax2 with respect to x-(a+1)x+1<0.

Solve simple fractional inequalities

Solve the following inequalities:

(1)x+23-x≥0; (2)2x-13-4x>1.

regular method

(1) When solving fractional inequalities, be sure to move the terms first so that the right-hand side becomes zero. Also note that the denominator of fractional inequalities containing an equal sign is not zero.

(2) Four forms of fractional inequalities and problem-solving ideas

①f(x)g(x)>0⇔f(x)g(x)>0;

②f(x)g(x)<0⇔f(x)g(x)<0;

③f(x)g(x)≥0⇔f(x)g(x)≥0 and g(x)≠0⇔f(x)g(x)>0 or f(x)=0;

Inequality PPT, Part 4: Feedback on Compliance

1. The solution set of inequality 3x2-7x+2<0 is ()

A.x132

C.x－122}

2. The solution set of inequality (3x-2)(2-x)≥0 is ()

A.23, 2 B.-∞, 23∪[2, +∞)

C.32,2 D.-23,2

3． The solution set of the inequality 4x+23x-1>0 is ()

A.x|x>13 or x<-12 B.x|-12

C.x|x>13 D.x|x<－12

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