Target Audience: High School Students, College Freshmen and Sophomores, Class 11/12 Students in India preparing for ISC/CBSE and Entrance Examinations like the IITJEE Main or Advanced/AIEEE, and anyone else who needs this Tutorial as a reference!After reading this tutorial you might want to check out some of our other Mathematics Quizzes as well. 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}+bx+c>0 or ax^{2}+bx+c<0 (or with the inequalities with the equal to sign)
The basic concepts in inequalities are:
Using this, if we have factorized the expression in the form: (xp)(xq),and p<q, then : if (xp)(xq)>0 then either xp>0 and xq>0 or xp<0 and xq<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 (xp)(xq)<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)
Here are the kind of questions covered in the tutorialQ: Solve x2+x+1<0
Q: Solve x2+4x>0
Q: Solve x2+5x+1>0.
Q: Solve x2+11x+24<0
Q: If x^{2}+kx+2=0 has real roots, what can be the possible values of k?
Tutorial with solved problems (To test your knowledge, try out the quiz at the end):MCQ Quiz/Worksheet for Quadratic InequationsYour score will be emailed to you at the address you provide. You might like to take a look at our other algebra tutorials:

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