Polynomial inequalities ppt

polynomial and rational inequalities ppt and polynomial and rational inequalities ppt
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Published Date:26-07-2017
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Polynomial inequalities MATH 1510 Lili Shen Polynomial and Rational Inequalities Systems of Linear Example Equations in Two Variables Solve the inequality 3 2 2x +x + 6 13x:Polynomial inequalities MATH 1510 Lili Shen Solution. Polynomial and Rational 3 2 Inequalities 2x +x 13x + 6 0; Systems of (x 2)(2x 1)(x + 3) 0: Linear Equations in Two Variables Checking the sign: 1 1 (1;3) (3; ) ( ; 2) (2;1) 2 2 x 2 + 2x 1 + + x + 3 + + + By checking the endpoints, we obtain the solution set 1 3; 2;1). 2Polynomial inequalities MATH 1510 3 2 The graph of f(x) = 2x +x 13x + 6 confirms our Lili Shen solution: Polynomial and Rational y Inequalities Systems of 60 Linear Equations in Two Variables 40 20 x 2 2 20Rational inequalities MATH 1510 Lili Shen Polynomial and Rational Inequalities Systems of Example Linear Equations in Two Variables Solve the inequality 1 2x  1: 2 x 2x 3Rational inequalities MATH 1510 Lili Shen Polynomial Solution. and Rational Inequalities Systems of 1 2x Linear 1 0; Equations in 2 x 2x 3 Two Variables 2 4x  0: 2 x 2x 3 2 x 4  0: 2 x 2x 3 (x 2)(x + 2)  0: (x 3)(x + 1)Rational inequalities MATH 1510 Lili Shen Checking the sign: Polynomial and Rational Inequalities (1;2) (2;1) (1; 2) (2; 3) (3;1) Systems of Linear x 3 + Equations in Two Variables x 2 + + x + 1 + + + x + 2 + + + + By checking the endpoints, we obtain the solution set 2;1)2; 3):Polynomial inequalities MATH 1510 2 x 4 The graph of f(x) = confirms our solution: Lili Shen 2 x 2x 3 Polynomial and Rational y Inequalities Systems of Linear 2 Equations in Two Variables x 4 2 2 4 2 4Outline MATH 1510 Lili Shen Polynomial and Rational Inequalities Systems of Linear 1 Polynomial and Rational Inequalities Equations in Two Variables 2 Systems of Linear Equations in Two VariablesSystems of linear equations and solutions MATH 1510 Lili Shen Polynomial and Rational Inequalities A linear equation in two variables x and y is an equation in Systems of the form of Linear Equations in ax +by = c; Two Variables where a;b;c2R are constants. A system of linear equations in two variables consists of several linear equations that involve the same variables.Systems of linear equations and solutions MATH 1510 Lili Shen Polynomial and Rational Here is an example of a system of linear equations in two Inequalities variables: ( Systems of Linear 2x y = 5 Equations in Two Variables x + 4y = 7 We can check that ( x = 3 y = 1 is a solution of this system.Systems of linear equations and solutions MATH 1510 In fact, (3; 1) is the coordinate of the intersection of the two Lili Shen lines: Polynomial and Rational y Inequalities x + 4y = 7 2xy = 5 Systems of Linear 2 Equations in (3; 1) Two Variables x 2 2 4 6 2 4Substitution method MATH 1510 Lili Shen Polynomial and Rational Inequalities Systems of Example Linear Equations in Find all solutions of the system Two Variables ( 2x + y = 1 (1) 3x + 4y = 14 (2)Substitution method MATH 1510 Lili Shen Solution. Polynomial and Rational From (1) one has y = 1 2x, and it follows from (2) that Inequalities Systems of Linear 3x + 4(1 2x) = 14; Equations in Two Variables 5x = 10; x =2: Hence ( x =2 y = 1 2(2) = 5 is the solution of the system.Elimination method MATH 1510 Lili Shen Polynomial and Rational Inequalities Systems of Example Linear Equations in Find all solutions of the system Two Variables ( 3x + 2y = 14 (1) x 2y = 2 (2)Elimination method MATH 1510 Lili Shen Solution. Polynomial By (1)+(2) one has and Rational Inequalities 4x = 16 Systems of Linear and thus x = 4. Hence Equations in Two Variables 4 2y = 2 and consequently y = 1. Therefore, ( x = 4 y = 1 is the solution of the system.The number of solutions MATH 1510 Lili Shen Polynomial and Rational Inequalities Systems of For a system of linear equations in two variables, exactly Linear one of the following is true: Equations in Two Variables 1 The system has exactly one solution. 2 The system has no solution. 3 The system has infinitely many solutions.A linear system with one solution MATH 1510 Lili Shen Polynomial and Rational Inequalities Systems of Example Linear Equations in Solve the system Two Variables ( 3x y = 0 (1) 5x + 2y = 22 (2)A linear system with one solution MATH 1510 Lili Shen Solution. Polynomial By 2(1)+(2) one has and Rational Inequalities Systems of 11x = 22 Linear Equations in Two Variables and thus x = 2. It follows that y = 3 2 = 6: Therefore, ( x = 2 y = 6 is the solution of the system.A linear system with no solution MATH 1510 Lili Shen Polynomial and Rational Inequalities Systems of Example Linear Equations in Solve the system Two Variables ( 8x 2y = 5 (1) 12x + 3y = 7 (2)A linear system with no solution MATH 1510 Lili Shen Polynomial and Rational Inequalities Systems of Solution. Linear Equations in By 3(1)+ 2(2) one has Two Variables 0 = 29: Thus the system has no solution.

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