Strategies for solving quadratic equations and inequalities in the JEE Main exam:

Quadratic equations and inequalities are an important topic in the mathematics section of the JEE Main exam. Here are some strategies to help you effectively solve questions related to quadratic equations and inequalities:

1. Understand the basics:
- Before attempting to solve quadratic equations and inequalities, it is crucial to have a clear understanding of their basic concepts.
- Familiarize yourself with the standard form of a quadratic equation: ax^2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0.

2. Identify the type of question:
- Determine whether the question asks for solving a quadratic equation or analyzing inequalities.
- For quadratic equations, you may be required to find the roots, determine the nature of roots, or solve them graphically.
- For inequalities, you may need to find the range of values that satisfy the given condition.

3. Factorization:
- One of the most common methods to solve quadratic equations is through factorization.
- Look for factors of the quadratic expression that can be equated to zero to find the roots.
- Practice different techniques of factorization, such as splitting the middle term or using the difference of squares.

4. Quadratic formula:
- Another important approach to solve quadratic equations is by using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).
- This formula allows you to find the roots of any quadratic equation, regardless of its factorability.
- Ensure that you are familiar with the quadratic formula and can apply it correctly in different scenarios.

5. Graphical method:
- Graphing quadratic equations can provide a visual representation of the roots and other important points.
- Use the concept of vertex, axis of symmetry, and discriminant to analyze the graph and solve related questions.

6. Inequalities:
- To solve quadratic inequalities, start by finding the critical points where the inequality changes.
- Use test points to determine the sign of the expression within each interval and identify the range of values that satisfy the inequality.

7. Practice and time management:
- Regular practice is crucial to enhance your problem-solving skills in quadratic equations and inequalities.
- Solve a variety of questions from previous years' papers and practice tests to familiarize yourself with different question patterns and techniques.
- Develop efficient time management strategies to allocate adequate time for each question during the exam.

By following these strategies, you can improve your problem-solving abilities and increase your chances of performing well in the quadratic equations and inequalities section of the JEE Main exam. Remember to practice regularly and seek clarification on any doubts or concepts that you find challenging. Good luck!