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messersmith_power_intermediate_algebra_1e_ch4_7_10

Procedure How to Solve a Quadratic Inequality Step 1: Write the inequality in the form ax2 bx c 0 or ax2 bx c 0. ( and may be substituted for and 0.) If the inequality symbol is or , we are looking for a negative quantity in the interval on the number line. If the inequality symbol is or , we are looking for a positive quantity in the interval. Step 2: Solve the equation ax2 bx c 0. Step 3: Put the solutions of ax2 bx c 0 on a number line. These values break up the number line into intervals. Step 4: Choose a test number in each interval to determine whether ax2 bx c is positive or negative in each interval. Indicate this on the number line. Step 5: If the inequality is in the form ax2 bx c 0 or ax2 bx c 0, then the solution set contains the numbers in the interval where ax2 bx c is negative. If the inequality is in the form ax2 bx c 0 or ax2 bx c 0, then the solution set contains the numbers in the interval where ax2 bx c is positive. Step 6: If the inequality symbol is or , then the endpoints of the interval(s) (the numbers found in Step 3) are included in the solution set. Indicate this with brackets in the interval notation. If the inequality symbol is or , then the endpoints of the interval(s) are not included in the solution set. Indicate this with parentheses in interval notation. 3 Solve Quadratic Inequalities with Special Solutions We should look carefully at the inequality before trying to solve it. Sometimes, it is not necessary to go through all of the steps. In your own words, summarize this procedure. EXAMPLE 3 Solve. a) (y 4)2 5 b) (t 8)2 3 Solution a) The inequality (y 4)2 5 says that a squared quantity, (y 4)2, is greater than or equal to a negative number, 5. This is always true. (A squared quantity will always be greater than or equal to zero.) Any real number, y, will satisfy the inequality. The solution set is (q, q). b) The inequality (t 8)2 3 says that a squared quantity, (t 8)2, is less than a negative number, 3. There is no real number value for t so that (t 8)2 3. The solution set is . YOU TRY 3 Solve. a) (k 2)2 4 b) (z 9)2 1 684 CHAPTER 10 Quadratic Equations and Functions www.mhhe.com/messersmith


messersmith_power_intermediate_algebra_1e_ch4_7_10
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