Class 11th Math-Unit 4 – Quadratic Equations

Exercise 4.1

Exercise 4.2

Exercise 4.3

Exercise 4.4

Exercise 4.5

Exercise 4.6

Exercise 4.7

Exercise 4.8

Exercise 4.9

Exercise 4.10

MCQ’s

Unit 4 of the Class 11th Mathematics syllabus is centered around quadratic equations, which are polynomial equations of the form ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0, where aaa, bbb, and ccc are constants and a≠0a \neq 0a=0. This unit delves into various methods of solving quadratic equations, the properties of their roots, and their applications in real-life situations.

Key Topics Covered:

Definition and Standard Form:
- Understanding what quadratic equations are and their standard form.
- Identifying coefficients aaa, bbb, and ccc.
Methods of Solving Quadratic Equations:
- Factoring: Expressing the quadratic equation as a product of its linear factors.
- Completing the Square: Rearranging the equation into a perfect square form to find its roots.
- Quadratic Formula: Using the formula x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}x=2a−b±b2−4ac to find the roots of the equation.
Nature of Roots:
- Determining the nature of the roots based on the discriminant D=b2−4acD = b^2 – 4acD=b2−4ac:
  - If D>0D > 0D>0: Two distinct real roots.
  - If D=0D = 0D=0: One real root (repeated).
  - If D<0D < 0D<0: No real roots (complex roots).
Graphical Representation:
- Understanding the graphical representation of quadratic equations as parabolas.
- Identifying the vertex, axis of symmetry, and the direction of the parabola (opening upwards or downwards).
Applications:
- Real-world applications of quadratic equations in areas such as physics, engineering, and finance.
- Word problems that can be modeled using quadratic equations.

Conclusion:

This unit provides a comprehensive understanding of quadratic equations, equipping students with the necessary skills to solve various mathematical problems. Mastery of quadratic equations is crucial for higher studies in mathematics and its applications across different fields