Solving quadratic inequalities

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1. Solving Quadratic Inequalities

2. 2 A quadratic inequality is a mathematical sentence in the form of ax 2 + bx + c > 0, that relates a quadratic expression using the inequality symbols , <, >, , or . To solve for quadratic inequalities, express the inequality in standard forn ; d etermine the boundary points; s et the intervals that will represent values to the left and right of the boundary points; p ick a test point for each interval and check which will make the inequality statement true; then w rite the solution for the inequality.  

3. 3 Example 1: Solve for the quadratic inequality of x 2 + 2 3x. ax 2 + bx + c > a. x 2 + 2 3x x 2 – 3x + 2 b. x 2 – 3x + 2 (x – 2)(x – 1) = 0 x – 2 = 0 x – 1 = 0 x = 2 x = 1 The boundary points are 1 and 2. The graph shows the possible interval solutions of the inequality. Since x can be equal to 1 or 2, there are possible intervals which illustrated as (- , 1], [1, 2], [2, + ).  

4. 4 the The solution to x 2 + 2 3x are the values of x that will make the product of the factors x – 1 and x – 2 greater than or equal to zero. We need to identify the interval/s that gives a result with positive sign. Thus the solutions are the intervals (- , 1 ] [2, + ).