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### Quadratic Inequalities - Using Factorization, Formulas and Plots of Curves- A Tutorial with Solved Problems and a Quiz at the end

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

, and anyone else who needs this Tutorial as a reference!

After understanding this topic, you might benefit from the MCQ Quiz over here.

### Quick Introduction (more detailed introduction in the tutorial document)

Quadratic inequalities refer to the inequalities of the type: ax22

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: (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)= ax2+bx+c when α<x< β, we have a negative value of f(x)

## MCQ Quiz/Worksheet for Quadratic In-equations

Your score will be e-mailed to you at the address you provide.

#### MCQ Companion Quiz- Quadratic Inequalities

 Introduction to Complex NumbersIntroduction to Complex Numbers and iota. Argand plane and iota. Complex numbers as free vectors. N-th roots of a complex number. Notes, formulas and solved problems related to these sub-topics. The Principle of Mathematical InductionIntroductory problems related to Mathematical Induction. Quadratic EquationsIntroducing 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 ProgressionsArithmetic, 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.

After reading this tutorial you might want to check out some of our other Mathematics Quizzes as well.
 Quizzes on ProgressionsMCQ #1: Arithmetic Progression MCQ #2: Geometric ProgressionMCQ #3 : More on Geometric Progressions.MCQ #4 : Harmonic Progressions. MCQ #5: More on Harmonic ProgressionMCQ #6: Mixed ProgressionsComplex NumbersMCQ #1MCQ #2: More on Complex NumbersQuadratic EquationsMCQ Quadratic EquationsQuadratic In-equationsMCQ Quadratic In-equations Coordinate Geometry - Straight LinesMCQ #1: Cartesian Planes, Straight Line BasicsMCQ #2 on Straight LinesMCQ #3 on Straight LinesMCQ #4 on Straight LinesCircles1 MCQ #1 on Circles. 2 MCQ #2 on Circles. 3 MCQ #3 on Circles. Conic Sections- Parabola, Hyperbola, Ellipse1 MCQ- The Basics of Conic Sections2 MCQ on Parabola..3 MCQ on Hyperbola4 MCQ on Ellipses. ProbabilityMCQ #1 on Basic ProbabilityMCQ #2: More Challenging Problems on ProbabilityMCQ #3- Conditional Probability and Bayes Theorem