Solutions Class 10 Chapter 2 By RS Aggarwal- Free PDF on Vedantu
FAQs on RS Aggarwal Solutions Class 10 Chapter 2 - Polynomials (Ex 2A) Exercise 2.1
1. What is the main focus of RS Aggarwal Solutions for Class 10 Maths Chapter 2, Exercise 2A?
The primary focus of Exercise 2A in RS Aggarwal's Class 10 Maths Chapter 2 is on two key skills: finding the zeros of a quadratic polynomial and then verifying the relationship between these zeros and their coefficients. The solutions guide students through methods like splitting the middle term to factorise polynomials and correctly applying the verification formulas.
2. What is the step-by-step method to find the zeros of a quadratic polynomial as shown in this exercise?
To find the zeros of a quadratic polynomial, you should follow this method:
1. Write the polynomial in the standard form ax² + bx + c and set it equal to zero.
2. Factorise the polynomial, typically by splitting the middle term (the 'bx' term).
3. Once you have two linear factors, set each factor equal to zero individually.
4. Solve each linear equation to find the two values of x. These values are the zeros of the polynomial.
3. What is the relationship between the zeros and coefficients of a quadratic polynomial that I need to use for verification?
For any quadratic polynomial ax² + bx + c, if its zeros are denoted by α (alpha) and β (beta), the relationship is as follows:
- Sum of Zeros (α + β) = -b/a, which is equivalent to -(Coefficient of x) / (Coefficient of x²).
- Product of Zeros (α × β) = c/a, which is equivalent to (Constant Term) / (Coefficient of x²).
4. Are the solutions for RS Aggarwal Chapter 2 sufficient for the Class 10 Board exam preparation?
RS Aggarwal provides an extensive set of questions that are excellent for building a strong foundation and practising a wide variety of problem types for Chapter 2, Polynomials. While it is highly recommended for thorough practice, it should be used as a supplement to the NCERT textbook, which is the prescribed book for the CBSE 2025-26 syllabus. Mastering both ensures comprehensive coverage for board exams.
5. Why is verifying the relationship between zeros and coefficients a necessary step?
Verifying the relationship between zeros and coefficients is a crucial step because it acts as a self-check mechanism to confirm your answer. If the sum and product of the zeros you calculated independently match the values derived from the coefficients using the formulas (-b/a and c/a), you can be confident that your factorisation and calculations are accurate. It reinforces your understanding of the fundamental structure of polynomials.
6. What is a common mistake when solving for zeros in a polynomial like x² – 5?
A common mistake when solving a polynomial where the 'bx' term is missing, such as x² – 5, is providing only the positive root. Students often incorrectly write x = √5 as the only solution. The correct method is to set x² = 5, which yields two solutions: x = +√5 and x = -√5. Forgetting the negative root is a frequent error that leads to an incomplete answer.
7. How can I form a quadratic polynomial if I only know the sum and product of its zeros?
If you are given the sum of the zeros (S) and the product of the zeros (P), you can construct the quadratic polynomial directly using the formula: x² – (Sum of zeros)x + (Product of zeros). This can be written as x² – Sx + P. This reverse process is a key concept in the chapter and is often asked in exams to test conceptual understanding.
8. How do the questions in RS Aggarwal Chapter 2 differ from the NCERT textbook for Polynomials?
The NCERT textbook establishes the core concepts and essential problems as per the CBSE syllabus. RS Aggarwal complements this by providing a much greater volume and variety of questions for practice. It helps students master the application of formulas through repetition and introduces slight variations in problems, which builds confidence and problem-solving speed for the board exams.
