Target Audience: High School Students, College Freshmen and Sophomores, Class 11/12 Students in India preparing for ISC/CBSE and Entrance Examinations like the IIT-JEE Main or Advanced/AIEEE, and anyone else who needs this Tutorial as a reference!After understanding this topic, you might benefit from the MCQ Quiz over here. Quadratic InequalitiesQuick Introduction (more detailed introduction in the tutorial document)Quadratic inequalities refer to the inequalities of the type: ax^{2}^{2} The basic concepts in inequalities are:
Using this, if we have factorized the expression in the form: (x-p)(x-q),and p<q, then : if (x-p)(x-q)>0 then either x-p>0 and x-q>0 or x-p<0 and x-q<0 =>x>p and x>q or x<p and x<q =>x>q or x<p (Because if x>p and x>q, then x>q is the common solution as p<q(Notice that “and” leads to taking the common solution, and “or” leads to unifying the solutions) ) Similarly, if (x-p)(x-q)<0 then, p<x<q. Clearly, when x<α and when x>β, we have a positive value of f(x), where f(x)= ax^{2}+bx+c when α<x< β, we have a negative value of f(x) Tutorial with solved problems (To test your knowledge, try out the quiz at the end):MCQ Quiz/Worksheet for Quadratic In-equationsYour score will be e-mailed to you at the address you provide.
After reading this tutorial you might want to check out some of our other Mathematics Quizzes as well. |
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