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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

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(ii) x² − 7x + 12

Solution

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(iii) 6x² − 3 − 7x

Solution

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(iv) 4u² + 8u

Solution

(v) t² − 15

Solution

(vi) 3x² − x − 4

Solution

Question 2

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

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(i)

Solution

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(ii)

Solution

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(iii)

Solution

(iv)

Solution

(v)

Solution

(vi)

Solution

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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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