RD Sharma Class 11 Chapter 14 Solutions (Quadratic Equations)
In previous chapters, we have studied Quadratic Equations with real coefficients and real roots only. However, in this chapter, we will study Quadratic Equations with real coefficients and complex roots. For better reasoning of the concepts, you can solve the exercise wise problems using the solutions, which are developed by our subject matter experts at InstaSolv.
Quadratic Equations are solved in three ways, by factorization method, by completing the square method and by formula method. We will also be understanding the nature of roots which is an integral part of the chapter
RD Sharma solutions have made sure that all the students get a chance to understand the above-mentioned topics as all of these topics are covered extensively in 39 questions divided into two exercises, exercise 14.1 and exercise 14.2 and with the help of Instasolv you can have a complete grasp of Quadratic Equations in a much simpler and understanding manner. There are also additional exercises named Exercise: VSA and Exercise: MCQ, which carries 20 more questions related to these topics.
Topics covered in RD Sharma Solutions for Class 11 Chapter 14 Quadratic Equations
In earlier chapters, we have learned that a quadratic equation is an equation in the form ax2 + bx + c = 0, where, a ≠ 0; However, what we learned was with real coefficients and real roots whereas, in this chapter, we will learn this with real coefficients but with complex roots as well.
To understand complex roots, we have to understand what a real polynomial is.
Let’s just take for an example, f(x)= a0+a1x+….anxn
Here, in the above equation a0 and a1 are real numbers, whereas x is a variable and a real coefficient. A complex variable is the same thing, but with a complex coefficient.
For example, 2×2- (3+7i)x+(9i-3)
Here, 2, 3+7i, 9i-3 are complex coefficients.
The degree of any polynomial is the highest power in any given equation, for example, it’s 2 in the above equation thus, making it a quadratic equation. If it’s power is 3 then it’s a cubic equation. If its power is 4 it’s a bi-quadratic equation, however, we will only be covering the quadratic equation.
There are three ways to solve Quadratic Equations, those are the factorization method, completing the square method and formulae method. However, our focus will be only on the factorization method. Factorization is the process of reducing the bracket and then solving the equation.
For example, let us take the following example.
The first step is to use the factoring strategies to factor the problem making it (z-2)(z-8)=0.
Using the Zero, product Property and setting each factor containing a variable equal to zero.
Identifying each factor which was set equal to a zero by having the z on one side and the answer on the other.
Most of the time we have to understand that all the Quadratic Equations cannot be solved this easily. Therefore, we have to understand the roots of the equations.
Let z and y be the roots of the quadratic equation zx2 + yx + c = 0. So, we can write:
z = (-y-√y2-4zc)/2z
y = (-y+√y2-4zc)/2z.
Here z, y, and c are real and rational. Hence, the nature of the roots z and y of equation zx2 + yx + c = 0 depends upon the quantity or expression (y2 – 4zc) under the square root sign. We can say this because the root of a negative number cannot be any real number.
Like, x2 = -1 is a quadratic equation. Here, there is no real number whose square is negative. So, for this equation, there can be no real number solutions.
Hence, the expression (y2 – 4zc) is called the discriminant of the quadratic equation zx2 + yx + c = 0.
Discussion on the Exercises of RD Sharma Solutions for Class 11 Chapter 14 Quadratic Equations
- Exercise 14.1 lays out the basic Quadratic Equations to be solved by the factorization method and contains 13 questions.
- Exercise 14.2 contains 2 questions with 16 parts with complex coefficients.
RD Sharma Class 11 Maths Solutions Maths Chapter 14 has been designed in such a way that it takes your knowledge up from what you have retained in Class 10. Thus, you will find it easy to grasp new concepts.
Benefits of RD Sharma Solutions for Class 11 chapter 14 sets by InstaSolv
With the help of InstaSolv, you will be able to understand all logic behind solving an equation and knowing the reasoning behind it. Our approach is focussed more towards active learning and critical thinking resulting in understanding the concept not just for exams but for practical applications as well.