RD Sharma Solutions for Class 10 Maths Chapter 8 - Quadratic Equations

The Quadratic formula provides the roots or zeros/x-intercepts of a quadratic equation. The quadratic equations are second-degree equations in x that have two answers for x. The two answers for x are the roots of the quadratic equations and are designed as (ɑ,β). Quadratic equations take the form of a parabola on the graph. Basically, the quadratic equation in its standard form is ax2+bx+c=0 where a and b are coefficients, x is the variable and c is the constant term. The first condition for an equation to be a quadratic equation is that the coefficient of x2  is not zero, i.e., a≠0. There are several forms of quadratic equations in real math problems like: 

a)  (x-1)(x+2)=0                                                              c) 5x(x+3)=12x

b)  -x2=-3x+1                                                                   d)  x3= x(x2+x-3)

All such equations have to be transformed into the standard form of quadratic equation before  moving forward with further operations. The quadratic formula is the easiest way to find the roots of a quadratic equation: x= [-b±√(b2-4ac)]/2a. When there are certain quadratic equations which cannot be easily factorised, here we can find the roots using this formula in the quickest possible way.

Surprisingly these complex-looking equations are used in the real world like in business to find the profit, to calculate room surface area during construction, in military and law enforcement for launching missiles and in sports to determine speed, height or velocity of a ball to be thrown by a player.

According to the latest (2024-25) version of R.D. Sharma Solutions for Class 10 Maths, Quadratic Equation features as the 8th Chapter of the textbook. It is one of the most important chapters of Class 10 Maths and can only be solved if the basics are strong and well- understood. It consists thirteen exercises *Exercises 8.1 to 8.13) after the chapter. The main modules included in this chapter are:

1. Determination and Formulation of Quadratic Equations

2. Various ways of finding their zeros/roots like factorisation, completing of square through Quadratic Equations

3. Application of Quadratic Equations in real life situations