NCERT Maths Chapter 4 Quadratic Equations – Solutions, Formula & Applications

Quadratic Equations are equations of degree two that play an important role in algebra and real-life problem-solving. They are used in mathematics, physics, engineering, and economics to model various situations.

This chapter is important for CBSE Board Exams and Competitive Exams.

What is a Quadratic Equation?

A quadratic equation is an equation of the form:

ax² + bx + c = 0

where a, b, and c are real numbers and a ≠ 0.

Methods of Solving Quadratic Equations

Factorization Method

In this method, the quadratic expression is factorized into two linear factors, and the values of the variable are obtained by equating each factor to zero.

Completing the Square

This method converts the quadratic equation into a perfect square form, making it easier to find the solution.

Quadratic Formula

A quadratic equation can also be solved using the quadratic formula, which provides direct solutions for the roots of the equation.

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Discriminant

The discriminant helps determine the nature of the roots of a quadratic equation.

Based on its value, the roots can be:

Real and Distinct
Real and Equal
Non-Real (Complex)

Applications of Quadratic Equations

Quadratic equations are used in:

Geometry problems
Motion and projectile calculations
Area and dimension calculations
Business and economics models

Importance of Quadratic Equations

Develops algebraic problem-solving skills.
Forms the basis for higher mathematics.
Helps solve real-life mathematical situations.
Widely used in science and engineering.

Importance for CBSE Exams

Quadratic Equations is a high-scoring chapter in NCERT Maths. Questions are commonly asked on factorization, quadratic formula, discriminant, and word problems based on quadratic equations.

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