RD SHARMA Solutions for Class 10 Mathematics Chapter 8: Quadratic Equations

This chapter deals with Quadratic equations, which are similar to the concept of quadratic polynomials, which we studied in Chapter 2- Polynomials. Quadratic polynomials, when equated with zero, are referred to as quadratic equations. Chapter 8- Quadratic Equations explains the method of representing situations and statements in the standard quadratic equation form to solve real-life problems.

It teaches students how to solve a given quadratic equation by the method of factorisation. This can be done by either direct factorisation based on the general formulae or by splitting the mid-term. The solutions obtained by factorisation are called the roots of the quadratic equations. The roots of a quadratic equation are the same as the zeroes of the equation.

Chapter 8- Quadratic Equations also sheds light on another method to solve quadratic equations, which involves completing the square of the variables present in the equation. This is done by introducing a set of constants on both the LHS and RHS, thereby rendering no change in the outcome of the equation, although it now enables us to rearrange the variables to form complete squares. Thus the rearranged equation can now easily be solved to find out the solution of the equation.

For example:

4x²+ 24x= -8

Adding 36 to both sides

4x²+ 24x+ 36= 28

(2x+6)² = 28

2x+ 6 = √28

Dividing by 2

x + 3 = √7

x = √7 - 3

A direct method to solve quadratic equations is also provided in the chapter. This can be achieved by virtue of the quadratic formula. It can be represented as follows:

For a given quadratic equation, ax² + bx² + c = 0;

The roots off the equation are given by, x=(-b±√(b²-4ac))/2a.

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