Introduction to Quadratic Equations and Inequations for JEE Main

The chapter Quadratic Equations and Inequations is a key topic in Class 11 Maths and forms the foundation for algebra, calculus, and coordinate geometry in JEE Main.

A quadratic equation is an equation of the form:
ax² + bx + c = 0, where a ≠ 0.
Solving quadratic equations and understanding their properties is essential for both conceptual and numerical JEE Main questions.

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Quadratic Equations

1. Standard Form: ax² + bx + c = 0

2. Roots of Quadratic Equation:
   Using quadratic formula: x = [-b ± √(b² – 4ac)] / 2a

   • Discriminant (Δ): Δ = b² – 4ac

   • Nature of roots:

     • Δ > 0 → Real and distinct roots

     • Δ = 0 → Real and equal roots

     • Δ < 0 → Complex roots

3. Relation Between Roots and Coefficients:

   • If roots are α and β:

     • α + β = –b/a

     • αβ = c/a

4. Methods of Solving Quadratic Equations:

   • Factorization

   • Completing the square

   • Quadratic formula

   • Graphical method

5. Symmetric Functions of Roots:

   • α² + β² = (α + β)² – 2αβ

   • α³ + β³ = (α + β)³ – 3αβ(α + β)

These formulas are frequently asked in JEE Main numerical and theoretical questions.

Quadratic Inequations

Quadratic inequations involve inequalities with quadratic expressions:

• ax² + bx + c > 0 or ax² + bx + c ≥ 0

• ax² + bx + c < 0 or ax² + bx + c ≤ 0

Steps to Solve Quadratic Inequalities:

1. Solve the corresponding quadratic equation ax² + bx + c = 0 to find roots α and β.

2. Draw a number line and mark the roots.

3. Determine the intervals where the quadratic expression is positive or negative.

Example: Solve x² – 5x + 6 > 0

• Roots: x² – 5x + 6 = 0 → x = 2, 3

• Solution: x < 2 or x > 3

Graphical Representation

• The graph of y = ax² + bx + c is a parabola

• If a > 0 → Opens upwards, minimum at vertex

• If a < 0 → Opens downwards, maximum at vertex

• Quadratic inequalities can be solved by observing the parabola relative to x-axis

Graphical understanding is very useful in JEE Main conceptual problems.

Applications of Quadratic Equations and Inequations

• Solving motion problems in physics

• Determining maximum and minimum values in algebra

• Solving word problems using quadratic forms

• Basis for higher-degree equations in calculus

JEE Main often tests these applications in numerical and MCQ format.

Important JEE Main Preparation Tips for Quadratics

• Memorize quadratic formula, discriminant, and relation between roots and coefficients

• Practice factorization and completing square methods

• Solve quadratic inequalities using number line and graph

• Use symmetric functions of roots for advanced problems

• Solve previous year JEE Main MCQs and numerical problems

Why Study Quadratic Equations and Inequations from Studentbro.in?

Studentbro.in provides:

• Step-by-step explanations of quadratic equations, roots, and inequalities

• Solved examples for factorization, formula method, and graphical solutions

• Charts and diagrams for quick revision

• MCQs and PYQs aligned with JEE Main syllabus

Conclusion

The Quadratic Equations and Inequations chapter is fundamental and scoring in Class 11 Maths for JEE Main. Mastery of solving quadratic equations, understanding the discriminant, relation between roots, and solving inequalities helps students tackle both conceptual and numerical problems efficiently.

Studentbro.in provides structured, easy-to-understand, and exam-focused content to master Quadratic Equations and Inequations effectively and boost JEE Main scores.