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Short Intro

In this post, students can find complete step-by-step solutions for Class 10 Maths Chapter 2 Polynomials Exercise 2.2 based on the latest NCERT syllabus. This exercise explains the relationship between zeroes and coefficients of quadratic polynomials in a simple and exam-oriented format.

Exercise 2.2 focuses on finding zeroes and verifying relationships between zeroes and coefficients of polynomials.

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Quick Information Box

Item	Details
Board	CBSE
Class	10
Subject	Maths
Chapter	Polynomials
Exercise	2.2
Main Topic	Relationship Between Zeroes & Coefficients

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Concepts Used (Topics Covered)

• Zeroes of Polynomial
• Quadratic Polynomial
• Sum of Zeroes
• Product of Zeroes
• Relationship Between Zeroes and Coefficients
• Factorisation Method

The chapter explains how zeroes of quadratic polynomials are related to coefficients.

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Important Formulas

General Quadratic Polynomial

$ax^2+bx+c$

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Sum of Zeroes

$\alpha+\beta=-\frac{b}{a}$

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Product of Zeroes

$\alpha\beta=\frac{c}{a}$

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Questions & Step-by-step Solutions

Question 1

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and coefficients.

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(i) x² − 2x − 8

Solution

Factorising:

x² − 2x − 8 = (x − 4)(x + 2)

Zeroes:

4 and −2

Verification:

Sum of zeroes:

4 + (−2) = 2

Using formula:

−b/a = −(−2)/1 = 2

Verified.

Product of zeroes:

4 × (−2) = −8

Using formula:

c/a = −8/1 = −8

Verified.

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(ii) x² − 7x + 12

Solution

Factorising:

x² − 7x + 12 = (x − 3)(x − 4)

Zeroes:

3 and 4

Verification:

Sum:

3 + 4 = 7

−b/a = −(−7)/1 = 7

Verified.

Product:

3 × 4 = 12

c/a = 12/1 = 12

Verified.

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(iii) 6x² − 3 − 7x

Solution

Rearranging:

6x² − 7x − 3

Factorising:

= (3x + 1)(2x − 3)

Zeroes:

−1/3 and 3/2

Verification:

Sum:

−1/3 + 3/2
= (−2 + 9)/6
= 7/6

Formula:

−b/a = −(−7)/6 = 7/6

Verified.

Product:

(−1/3)(3/2) = −1/2

Formula:

c/a = −3/6 = −1/2

Verified.

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Question 2

Find a quadratic polynomial whose zeroes are:

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(i) 2 and −3

Solution

Polynomial:

$x^2-(\alpha+\beta)x+\alpha\beta$

Substituting values:

x² − (2 − 3)x + (2)(−3)

x² + x − 6

Final Answer:

x² + x − 6

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(ii) √2 and −√2

Solution

Sum:

√2 + (−√2) = 0

Product:

√2 × (−√2) = −2

Polynomial:

x² − 0x − 2

x² − 2

Final Answer:

x² − 2

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(iii) √3 and 1/√3

Solution

Sum:

√3 + 1/√3

Taking LCM:

= (3 + 1)/√3
= 4/√3

Product:

√3 × 1/√3 = 1

Polynomial:

x² − (4/√3)x + 1

Multiplying by √3:

√3x² − 4x + √3

Final Answer:

√3x² − 4x + √3

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Common Mistakes

• Wrong sign in sum formula
• Incorrect factorisation
• Forgetting to simplify fractions
• Confusing product and sum formulas

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Exam Tips

• Learn formulas properly.
• Verify answers carefully.
• Always write factorisation steps.
• Practice sign handling regularly.

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Practice MCQs

MCQ 1

For polynomial ax² + bx + c:

α + β equals:

A. c/a
B. −b/a
C. b/a
D. −c/a

Answer:

B. −b/a

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MCQ 2

If zeroes are 2 and 3, product is:

A. 5
B. 6
C. 1
D. 0

Answer:

B. 6

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MCQ 3

A quadratic polynomial has:

A. 1 zero
B. 2 zeroes
C. 3 zeroes
D. Infinite zeroes

Answer:

B. 2 zeroes

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MCQ 4

For x² − 5x + 6, sum of zeroes is:

A. 5
B. −5
C. 6
D. −6

Answer:

A. 5

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FAQ Section

What is the relationship between zeroes and coefficients?

For ax² + bx + c:

$\alpha+\beta=-\frac{b}{a}$​

and

$\alpha\beta=\frac{c}{a}$

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Why is Exercise 2.2 important?

It forms the base for quadratic equations and board exam questions.

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Can quadratic polynomials have irrational zeroes?

Yes, quadratic polynomials can have irrational zeroes.

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Which method is mostly used in Exercise 2.2?

Factorisation method.

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