11/19/2022 0 Comments Solving quadratic inequalities![]() Now since the inequality (x 2)(x-2)(x-3) > 0, we need to consider the positive regions on the number line. Plotting the factors on the number line and alternating and – starting from the rightĬapture 1.PNG Since the inequality here is (x-2) (x-3) 0 with factors -2, 2 and 3. If the inequality is of the form ax^2 bx c 0 the region having the sign will be the solutions of the given quadratic inequality. If we consider any value to the left of 2 then the product (x-2) (x-3) will always be positive.Ĥ. If we consider any value in between 2 and 3 then the product (x-2) (x-3) will always be negative. If we consider any value to the right of 3 then the product (x-2) (x-3) will always be positive. Placing factors 2 and 3 on the number lineĬapture.PNG Why the alternating and – signs from the right hand side you may ask? Start from the right and mark the region with sign, the next region with a – sign and the third region with a sign (alternating and - starting from the right). The number line will get divided into the three regions. If the inequality is not in the standard form then rewrite the inequality so that all nonzero terms appear on one side of the inequality sign.Īdding 6 on both sided of the above inequality we get x^2 – 5x 6 (x-2) (x-3) < 0Ģ and 3 are the factors of the inequality.ģ. Let us consider the quadratic inequality x^2 – 5x 0). The standard quadratic equation becomes an inequality if it is represented as ax^2 bx c 0). Once mastered, this concept can be used for any inequality involving polynomials and makes solving a complex inequality question, a mere walk in the park.īefore we start, let us recall that the standard form of a quadratic equation is ax^2 bx c = 0. Quadratic inequalities are an important and often overlooked concept on the GMAT. "img": "/forum/images/mba_dashboard/image_5.png", #Solving quadratic inequalities free#"helpContent": " Sign up for AdCom Q
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