Quadratic Equations - Ex 4.2 NCERT Solutions

Quadratic equations are polynomial equations of second degree. It can be represented in the form of ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. In this chapter, we will learn how to solve quadratic equations by different methods.

Methods of solving quadratic equations:

1. Factorization Method:
In this method, we factorize the quadratic equation into two linear factors. For example, if we have to solve the equation x² + 5x + 6 = 0, we can factorize it as (x + 2) (x + 3) = 0. Then, by equating each factor to zero, we get the value of x.

2. Completing the Square Method:
In this method, we convert the given quadratic equation into a perfect square. For example, if we have to solve the equation x² + 6x - 7 = 0, we can convert it into (x + 3)² - 16 = 0. Then, by adding 16 on both sides and taking the square root, we get the value of x.

3. Quadratic Formula Method:
In this method, we use the quadratic formula to find the value of x. The quadratic formula is x = (-b ± √(b² - 4ac)) / 2a. For example, if we have to solve the equation 2x² + 5x - 3 = 0, we can use the quadratic formula to find the value of x.

Importance of Quadratic Equations:
Quadratic equations are important in many fields of mathematics and science. They are used in engineering, physics, chemistry, economics, computer science, and many other fields. For example, in physics, quadratic equations are used to solve problems related to motion, forces, and energy. In economics, quadratic equations are used to solve problems related to profit, cost, and revenue.

Conclusion:
Quadratic equations are important in various fields of mathematics and science. We can solve them by different methods such as factorization, completing the square, and quadratic formula. It is essential to understand the concepts of quadratic equations to solve complex problems in different fields.