Polynomials Class 10 Important Questions - Free PDF

Polynomials Class 10 Important Questions: Polynomials are a part of our daily life more than we realise. They are used in the design of roller coasters, slopes of hills, bridges, and even mountain ranges. Engineers depend on polynomial equations to make sure their structures, like bridges, remain strong and balanced. In Class 10 Maths, Chapter 2 helps you understand what polynomials are, how to classify them, and how to apply important formulas. This chapter builds the base for many higher-level concepts in mathematics.

To support your preparation, PW Store is offering a free PDF that includes class 10 polynomials important questions. You’ll also get plenty of chapter 2 class 10 maths extra questions and practice sets made to match exam patterns. These class 10 polynomials extra questions will help you test your understanding and improve your problem-solving speed. If you’re looking for helpful ch 2 Maths Class 10 extra questions to revise and score better, this is the right place to begin. Download the PDF today and boost your preparation.

Check Out: CBSE Class 10 Books

Polynomials Formulas

Go through the Polynomials Formulas here:- 

Check Out: CBSE Class 10 Question Banks

Polynomials Class 10 Important Questions

To help you prepare better, PW (Physics Wallah) is offering a free PDF of Class 10 Polynomials Important Questions. It includes well-selected questions based on the latest CBSE pattern, along with class 10 polynomials extra questions for thorough revision. 

Whether you're revising concepts or practising for the final exam, this resource from PW will help you strengthen your basics and boost your confidence.

Below we have provided Important Questions for Class 10 Maths Chapter 2 to help students prepare better for their Class 10 maths exams. Students can prepare these Important Questions for Class 10 Maths Chapter 2 Polynomials before their exams to understand the concepts better.

Q.1: Find the value of “p” from the polynomial x ² + 3x + p, if one of the zeroes of the polynomial is 2.

Solution:

As 2 is the zero of the polynomial.

We know that if α is a zero of the polynomial p(x), then p(α) = 0 Substituting x = 2 in x ² + 3x + p, ⇒ 2 ² + 3(2) + p = 0 ⇒ 4 + 6 + p = 0 ⇒ 10 + p = 0 ⇒ p = -10

Q.2: Does the polynomial a ⁴ + 4a ² + 5 have real zeroes?

Solution:

In the given polynomial, let a ² = x.

Now, the polynomial becomes, x  ² + 4x + 5 Comparing with ax ² + bx + c, Here, b ² – 4ac = 4 ² – 4(1)(5) = 16 – 20 = -4

So, D = b  ² – 4ac < 0 As the discriminant (D) is negative,

the given polynomial does not have real roots or zeroes.

Q.3: Compute the zeroes of the polynomial 4x ² – 4x – 8. Also, establish a relationship between the zeroes and coefficients.

Solution:

Let the given polynomial be

p(x) = 4x  ² – 4x – 8

To find the zeroes, take p(x) = 0 Now,

factorise the equation 4x  ² – 4x – 8 = 0 4x ² – 4x – 8 = 0 4(x ² – x – 2) = 0 x ² – x – 2 = 0 x ² – 2x + x – 2 = 0 x(x – 2) + 1(x – 2) = 0 (x – 2)(x + 1) = 0 x = 2, x = -1

So, the roots of 4x  ² – 4x – 8 are -1 and 2.

Relation between the sum of zeroes and coefficients: -1 + 2 = 1 = -(-4)/4

i.e. (- coefficient of x/ coefficient of x  ² ) Relation between the product of zeroes and coefficients: (-1) × 2 = -2 =  -8/4 i.e (constant/coefficient of x ² )

Q.4: Find the quadratic polynomial if its zeroes are 0, √5.

Solution:

A quadratic polynomial can be written using the sum and product of its zeroes as:

 x ² – (α + β)x + αβ Where α and β are the roots of the polynomial. Here, α = 0 and β = √5 So, the polynomial will be: x ² – (0 + √5)x + 0(√5) = x ² – √5x

Q.5: Find the value of “x” in the polynomial 2a ² + 2xa + 5a + 10 if (a + x) is one of its factors.

Solution:

Let f(a) = 2a ² + 2xa + 5a + 10 Since, (a + x) is a factor of 2a ² + 2xa + 5a + 10, f(-x) = 0 So, f(-x) = 2x ² – 2x ² – 5x + 10 = 0 -5x + 10 = 0 5x = 10 x = 10/5

Therefore, x = 2

Q.6: How many zeros does the polynomial (x – 3) ² – 4 have? Also, find its zeroes.

Solution:

Given polynomial is (x – 3) ² – 4

Now, expand this expression. => x  ² + 9 – 6x – 4 = x ² – 6x + 5

 As the polynomial has a degree of 2, the number of zeroes will be 2. Now, solve x ² – 6x + 5 = 0 to get the roots. So, x ² – x – 5x + 5 = 0 => x(x – 1) -5(x – 1) = 0 => (x – 1)(x – 5) = 0 x = 1, x = 5 So, the roots are 1 and 5.

Q.7: α and β are zeroes of the quadratic polynomial x ² – 6x + y. Find the value of ‘y’ if 3α + 2β = 20.

Solution:

Let, f(x) = x² – 6x + y From the given, 3α + 2β = 20———————(i) From f(x), α + β = 6———————(ii) And, αβ = y———————(iii) Multiply equation

(ii) by 2. Then, subtract the whole equation from equation (i), => α = 20 – 12 = 8 Now, substitute this value in equation (ii), => β = 6 – 8 = -2 Substitute the values of α and β in equation (iii) to get the value of y, such as; y = αβ = (8)(-2) = -16

Q.8: If the zeroes of the polynomial x ³ – 3x ² + x + 1 are a – b, a, a + b, then find the value of a and b.

Solution:

Let the given polynomial be: p(x) = x ³ – 3x ² + x + 1 Given, The zeroes of the p(x) are a – b, a, and a + b.

Now, compare the given polynomial equation with general expression. px  ³ + qx ² + rx + s = x ³ – 3x ² + x + 1 Here, p = 1, q = -3, r = 1 and s = 1 For sum of zeroes: Sum of zeroes will be = a – b + a + a + b -q/p = 3a Substitute the values q and p. -(-3)/1 = 3a a = 1

So, the zeroes are 1 – b, 1, 1 + b. For the product of zeroes: Product of zeroes = 1(1 – b)(1 + b) -s/p = 1 – 𝑏  ² => -1/1 = 1 – 𝑏 ² Or, 𝑏 ² = 1 + 1 =2 So, b = √2 Thus, 1 – √2, 1, 1 + √2 are the zeroes of equation 𝑥 ³ − 3𝑥 ² + 𝑥 + 1.

Q.9: Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes, respectively.

(i) 1/4, -1

(ii) 1, 1

(iii) 4, 1

Solution:

(i) From the formulas of sum and product of zeroes, we know, Sum of zeroes = α + β Product of zeroes = αβ Given, Sum of zeroes = 1/4 Product of zeroes = -1

Therefore, if α and β are zeroes of any quadratic polynomial, then the polynomial can be written as:- x  ² – (α + β)x + αβ = x ² – (1/4)x + (-1) = 4x ² – x – 4 Thus, 4x ² – x – 4 is the required quadratic polynomial.

(ii) Given, Sum of zeroes = 1 = α + β Product of zeroes = 1 = αβ Therefore, if α and β are zeroes of any quadratic polynomial, then the polynomial can be written as:- x ² – (α + β)x + αβ = x ² – x + 1

Thus, x  ² – x + 1 is the quadratic polynomial.

(iii) Given, Sum of zeroes, α + β = 4 Product of zeroes, αβ = 1 Therefore, if α and β are zeroes of any quadratic polynomial, then the polynomial can be written as:- x ² – (α + β)x + αβ = x ² – 4x + 1

Thus, x  ² – 4x +1 is the quadratic polynomial.

Q.10: Obtain all other zeroes of 3x ⁴ + 6x ³ – 2x ² – 10x – 5, if two of its zeroes are √(5/3) and-√(5/3).

Solution: Since this is a polynomial of degree 4, hence there will be a total of 4 roots.

√(5/3) and-√(5/3) are zeroes of polynomial f(x). ∴ [x-√(5/3)] [x+√(5/3)] = x ² -(5/3) Therefore, 3x ² + 6x + 3 = 3x(x + 1) +3 (x + 1) = (3x + 3)(x + 1) = 3(x + 1)(x + 1) = 3(x + 1)(x + 1) Hence, x + 1 = 0 i.e. x = – 1 , – 1 is a zero of p(x).

So, its zeroes are given by: x = −1 and x = −1.

Therefore, all four zeroes of the given polynomial are:

√(5/3) and-√(5/3), −1 and −1.

Click the link below and get the Polynomials Class 10 Important Questions. 

Polynomials Class 10 Important Questions PDF

Summary of Polynomials 

Chapter 2 of Class 10 Maths, titled Polynomials, is an important part of algebra. A polynomial is an expression that includes variables, constants, and mathematical operations like addition, subtraction, and multiplication. 

1. Types of Polynomials: Based on the number of terms (monomial, binomial, trinomial) and degree (linear, quadratic, cubic).

2. Degree of a Polynomial: The highest power of the variable.

3. Zeroes of a Polynomial: The values of 𝑥 for which the polynomial becomes zero.

4. Relationship Between Zeros and Coefficients: For quadratic and cubic polynomials, students learn how to relate the zeroes to the sum and product of coefficients.

5. Geometrical Meaning of Zeroes: Understanding how the graph of a polynomial intersects the x-axis.

6. Division Algorithm: Applying the division method to divide polynomials and verify the result.

Check Out: CBSE Class 10 Mind Maps Book For 2026 Board Exams

How to Solve Chapter 2 Class 10 Maths Extra Questions?

Solving class 10 polynomials extra questions correctly can make a significant difference in your exam preparation. Chapter 2 deals with concepts like types of polynomials, zeroes, relationships between zeroes and coefficients, and the division algorithm. These topics are not only important for exams but also useful in future classes. Here are some practical tips to help you handle ch 2 Maths Class 10 extra questions effectively:

1. Start with NCERT Basics

Before jumping into chapter 2 class 10 maths extra questions, revise the entire NCERT chapter. Make sure you understand what a polynomial is, how to identify its degree, and how to apply the standard formulas.

2. Make a Formula List

Keep a small notebook where you write down all formulas related to class 10 polynomials and important questions. This includes formulas for the sum and product of zeroes and basic terms used in polynomial expressions.

3. Solve Questions Topic-Wise

Break the class 10 maths chapter 2 important questions into sections. Focus on one concept at a time, such as identifying degrees, classifying polynomials, or applying the division algorithm. This helps you avoid confusion and gives you clarity.

Also Check: CBSE Class 10 Sample Papers

4. Keep a Timer

Time management is important. When solving ch 2 Maths Class 10 important questions, try to solve each question within a set time limit. This builds speed and confidence for the exam.

5. Work on Mistakes

After completing a set of Chapter 2 class 10 maths extra questions, review your mistakes. Understand why you made them and note them down. Avoid repeating the same errors in future practice.

6. Use Step-by-Step Solving

Always write steps clearly. In board exams, marks are given not only for correct answers but also for the method. Practising ch 2 Maths Class 10 extra questions step-by-step helps you get into the habit of proper presentation.

7. Revise Regularly

Revisiting previously solved class 10 polynomials extra questions every few days helps you remember the method and avoid forgetting formulas or concepts.

Read More: NCERT Solutions for Class 10 Maths Chapter 2 Polynomials

Polynomials Class 10 Important Questions FAQs

1. What is the best way to start preparing for Class 10 Polynomials?

Start by reading and understanding the NCERT textbook. Then move on to solving class 10 polynomials extra questions to test your understanding.

2. Are the NCERT questions enough for Chapter 2 Polynomials?

NCERT is the base, but solving chapter 2 class 10 maths extra questions will give you more practice and help you handle tricky questions in exams.

3. Why should I solve extra questions from this chapter?

Ch 2 maths class 10 extra questions cover different formats and difficulty levels, improving your speed, clarity, and accuracy.

4. Where can I get Class 10 Polynomials Important Questions in PDF format?

You can download the free PDF from trusted platforms like PW Store that provide quality ch 2 maths class 10 important questions for revision.

5. How do I remember the formulas for this chapter?

Make a formula sheet and revise it regularly. Apply the formulas while solving class 10 maths chapter 2 important questions.