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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!
Quadratic Inequalities
Quick 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:
 if ab>0 then either a>0 and b>0 or a<0 and b<0.
 if ab<0 then either a>0 and b<0 or a<0 and b>0.
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 tutorial
Q: 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. MCQ Companion Quiz Quadratic InequalitiesGoogle Spreadsheet Form
You might like to take a look at our other algebra tutorials:
Introduction to Complex Numbers Introduction to Complex Numbers and iota. Argand plane and iota. Complex numbers as free vectors. Nth roots of a complex number. Notes, formulas and solved problems related to these subtopics. 
The Principle of Mathematical Induction Introductory problems related to Mathematical Induction. 
Quadratic Equations Introducing various techniques by which quadratic equations can be solved  factorization, direct formula. Relationship between roots of a quadratic equation. Cubic and higher order equations  relationship between roots and coefficients for these. Graphs and plots of quadratic equations. 
Quadratic Inequalities Quadratic inequalities. Using factorization and visualization based methods. 
Series and Progressions Arithmetic, Geometric, Harmonic and mixed progressions. Notes, formulas and solved problems. Sum of the first N terms. Arithmetic, Geometric and Harmonic means and the relationship between them. 



