Quadratic Equations and Theory of Equations are important topics in the Class 12 syllabus, particularly for students preparing for JEE exams. Understanding these concepts thoroughly will help you solve complex mathematical problems and equations effectively.


Quadratic Equations are polynomial equations of degree 2, which can be written in the standard form as ax^2 + bx + c = 0, where a, b, and c are constants. To study quadratic equations and their properties, follow these steps:

1. Study the basic properties:
- Quadratic equations have either two distinct real roots, two identical real roots, or no real roots.
- The discriminant (b^2 - 4ac) determines the nature of roots. If the discriminant is positive, the equation has two distinct real roots. If it is zero, the equation has two identical real roots. If it is negative, the equation has no real roots.

2. Learn the quadratic formula:
- The quadratic formula is x = (-b ± √(b^2 - 4ac))/(2a).
- It is used to find the roots of any quadratic equation. By substituting the values of a, b, and c in the formula, you can calculate the roots.

3. Understand the graphical representation:
- Quadratic equations can be represented graphically as parabolas.
- The vertex of the parabola is the minimum or maximum point of the equation, depending on whether the coefficient of x^2 is positive or negative.


Theory of Equations deals with the study of polynomial equations of any degree. To understand this topic, follow these steps:

1. Study the fundamental theorem of algebra:
- The fundamental theorem of algebra states that every polynomial equation of degree 'n' has 'n' complex roots, including repeated roots.
- It helps in understanding the number of roots a polynomial equation can have.

2. Learn about the properties of roots:
- Vieta's formulas provide a relationship between the coefficients of a polynomial equation and its roots.
- By understanding these formulas, you can find the sum and product of the roots, as well as the relationships between the roots and coefficients.

3. Explore equations of higher degrees:
- Apart from quadratic equations, the theory of equations also covers equations of higher degrees such as cubic, quartic, and so on.
- Study the methods to solve these higher-degree equations, including the use of synthetic division, factor theorem, and rational root theorem.


To access comprehensive study material, including theory, solved examples, practice questions, and more, you can visit the EduRev website. They provide a wide range of resources specifically designed for Class 12 students preparing for JEE exams. Simply search for "quadratic equations" and "theory of equations" on the EduRev platform, and you will find relevant study material to enhance your understanding.

Remember to practice solving various types of quadratic equations and polynomial equations to strengthen your grasp on the concepts. Regular practice and thorough understanding will help you excel in your Class 12 exams and JEE preparations.