An Overview of Class 10 Maths Polynomials Worksheets
FAQs on Class 10 Maths Polynomials Worksheets
1. What are the most important types of questions to practice from Chapter 2, Polynomials, for the CBSE Class 10 Board Exam 2025-26?
For the Class 10 board exam, the most important questions from Polynomials focus on a few key areas based on the NCERT syllabus. You should prioritise practising:
Finding the zeros of a quadratic polynomial by splitting the middle term.
Verifying the relationship between the zeros and the coefficients of a quadratic polynomial.
Forming a quadratic polynomial when the sum and product of its zeros are given.
Solving questions where you need to find the value of a missing coefficient (like 'k') when a zero or a relationship between zeros is provided.
Higher Order Thinking Skills (HOTS) questions involving symmetric expressions of zeros (e.g., finding α² + β²).
2. What is the expected weightage for Chapter 2, Polynomials, in the Class 10 Maths exam, and are there any recurring question patterns?
Chapter 2, Polynomials, is part of the 'Algebra' unit, which holds a significant weightage of approximately 20 marks in the CBSE Class 10 Maths board exam. While the exact marks for this specific chapter can vary, you can typically expect questions worth 2 to 3 marks. The most frequently asked question type over the years has been on the relationship between zeros and coefficients, making it a very important topic for scoring well.
3. How are questions on the relationship between zeros (α, β) and coefficients typically framed in the board exam?
In the exam, questions on this topic are designed to test your understanding of the formulas: Sum of zeros (α + β) = -b/a and Product of zeros (αβ) = c/a. Common formats include:
Verification Questions: You will be asked to first find the zeros of a given polynomial and then verify this relationship.
Evaluation Questions: Given a polynomial, you will be asked to find the value of an expression like 1/α + 1/β without finding the actual zeros.
Problem-Solving Questions: You might be given a condition (e.g., one zero is the reciprocal of the other) and asked to find the value of an unknown coefficient in the polynomial.
4. What is the correct method for a 2-mark question on forming a quadratic polynomial when its zeros are known?
For a 2-mark question, the expected method is to use the standard formula: p(x) = k[x² – (sum of zeros)x + (product of zeros)], where 'k' is any non-zero real number. The steps are:
First, calculate the sum of the zeros (α + β).
Next, calculate the product of the zeros (αβ).
Substitute these values into the formula. Unless specified, you can assume k=1 for the simplest form of the polynomial. Marks are awarded for correctly stating the formula and substituting the calculated values.
5. If α and β are the zeros of a quadratic polynomial, how can we solve important questions that ask for values like α² + β² or 1/α + 1/β without actually finding the zeros?
This is a classic Higher Order Thinking Skills (HOTS) question. The key is to use algebraic identities to express the required expression in terms of (α + β) and (αβ). You can find these two values directly from the polynomial using -b/a and c/a. The conversions are:
For α² + β², use the identity: (α + β)² - 2αβ.
For 1/α + 1/β, first take the LCM to get (α + β) / αβ.
For α³ + β³, use the identity: (α + β)³ - 3αβ(α + β).
This method is faster and less prone to calculation errors than finding the zeros individually.
6. What is a common mistake students make when solving important questions on finding zeros and their relationships with coefficients?
A very common but critical mistake is not ensuring the polynomial is in its standard form (ax² + bx + c) before identifying the coefficients a, b, and c. For instance, if the polynomial is given as x² - 5 + 4x, many students incorrectly take a=1, b=-5, and c=4. The correct first step is to rearrange it to x² + 4x - 5. Only then can you correctly identify a=1, b=4, and c=-5 to apply the relationship formulas accurately.
7. Why is understanding the relationship between zeros and coefficients considered so important for the Class 10 exam?
This relationship is a central concept in algebra and is highly important for the exam because it tests your conceptual understanding beyond simple calculation. It allows you to deduce properties of a polynomial's roots without actually solving for them. This is a powerful tool for:
Verifying answers quickly during the exam.
Solving complex problems (HOTS) efficiently.
Building a strong foundation for more advanced topics in Class 11 and 12, where analysing polynomial functions is crucial.
8. What is the most frequently tested method for finding the zeros of a quadratic polynomial in the board exam?
For the CBSE Class 10 exam, the primary and most frequently tested algebraic method for finding the zeros of a quadratic polynomial is factorisation by splitting the middle term. The standard procedure involves:
Equating the polynomial p(x) to zero.
Splitting the middle term 'bx' into two terms whose sum is 'b' and whose product is 'ac'.
Factoring the expression into two linear factors.
Equating each factor to zero to find the two zeros.
This method is a core skill expected from this chapter.
