NCERT Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.2 Solutions (2026-27)

Looking for the most accurate NCERT Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.2 solutions? In this post, we provide step-by-step answers for Exercise 2.2, covering linear and quadratic polynomial values along with real-world algebraic applications.

These solutions are updated for the new 2026-27 NCERT syllabus to help students master equation solving and polynomial evaluations.

Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.2 Solutions

Exercise 2.2 - Question 1

Find the value of the linear polynomial \( 5x - 3 \) if:

(i)  When  \( x = 0 \): 

\( 5(0) - 3 = 0 - 3 = \mathbf{-3} \)

(ii) When \( x = -1 \): 

\( 5(-1) - 3 = -5 - 3 = \mathbf{-8} \)

(iii) When \( x = 2 \): 

\( 5(2) - 3 = 10 - 3 = \mathbf{7} \)

Exercise 2.2 - Question 2

Find the value of the quadratic polynomial \( 7s^2 - 4s + 6 \) if:

(i) When  \( s = 0 \): 

\( 7(0)^2 - 4(0) + 6 = 0 - 0 + 6 = \mathbf{6} \)

(ii) When \( s = -3 \): 

\( 7(-3)^2 - 4(-3) + 6 = 7(9) + 12 + 6 = 63 + 18 = \mathbf{81} \)

(iii) When \( s = 4 \): 

\( 7(4)^2 - 4(4) + 6 = 7(16) - 16 + 6 = 112 - 16 + 6 = \mathbf{102} \)

Exercise 2.2 - Question 3

The present age of Salil’s mother is three times Salil’s present age. After 5 years, their ages will add up to 70 years. Find their present ages.

Solution

Let Salil's present age = \( x \) years.
Mother's present age = \( 3x \) years.

After 5 years:
\( (x + 5) + (3x + 5) = 70 \)
\( 4x + 10 = 70 \)
\( 4x = 60 \)
\( x = 15 \)

Salil's age = 15 years
Mother's age = 3(15) = 45 years

Exercise 2.2 - Question 4

The difference between two positive integers is 63. The ratio of the two integers is 2:5. Find the two integers.

Solution

Let the integers be \( 2x \) and \( 5x \).
According to the question:

\( 5x - 2x = 63 \)
\( 3x = 63 \)
\( x = 21 \)

First integer = 2(21) = 42
Second integer = 5(21) = 105

Exercise 2.2 - Question 5

Ruby has 3 times as many two-rupee coins as she has five rupee-coins. If she has a total ₹88, how many coins does she have of each type?

Solution

Let number of ₹5 coins = \( x \).
Number of ₹2 coins = \( 3x \).

Total Value = \( 5(x) + 2(3x) = 88 \)
\( 5x + 6x = 88 \)
\( 11x = 88 \)
\( x = 8 \)

₹5 coins = 8
₹2 coins = 3(8) = 24

Exercise 2.2 - Question 6

A farmer cuts a 300 feet fence into two pieces of different sizes. The longer piece is four times as long as the shorter piece. How long are the two pieces?

Solution

Let the shorter piece = \( x \) feet.
Longer piece = \( 4x \) feet.

\( x + 4x = 300 \)
\( 5x = 300 \)
\( x = 60 \)

Shorter piece = 60 feet
Longer piece = 4(60) = 240 feet

Exercise 2.2 - Question 7

If the length of a rectangle is three more than twice its width and its perimeter is 24 cm, what are the dimensions of the rectangle?

Solution

Let width = \( x \) cm.
Then, Length = \( 2x + 3 \) cm.

Perimeter = \( 2(Length + Width) \)
\( 24 = 2[(2x + 3) + x] \)
\( 12 = 3x + 3 \)
\( 9 = 3x \)
\( x = 3 \)

Width = 3 cm
Length = 2(3) + 3 = 9 cm

Frequently Asked Questions (FAQs)

1. What is the value of a polynomial at a given point?

The value of a polynomial \( p(x) \) at \( x = a \) is obtained by substituting 'a' in place of 'x' throughout the expression and simplifying it.

2. How do you find the zero of a linear polynomial?

To find the zero of a linear polynomial, set the expression equal to zero (\( p(x) = 0 \)) and solve for the variable \( x \).

3. Are Ganita Manjari Class 9 solutions updated for 2026-27?

Yes, these solutions are strictly based on the latest NCERT Ganita Manjari textbook released for the 2026-27 academic session.

4. Can a zero of a polynomial be 0 itself?

Yes, if substituting \( x = 0 \) makes the entire polynomial value 0, then 0 is a zero of that polynomial.

5. How many zeros can a quadratic polynomial have?

A quadratic polynomial (degree 2) can have at most two zeros.

6. What are real-world applications of finding polynomial zeros?

It is used to solve age problems, calculate dimensions of shapes (like rectangles), and determine unknown quantities in finance, as seen in Exercise 2.2 word problems.

7. Is every real number a zero of a zero polynomial?

Yes, for a zero polynomial \( p(x) = 0 \), every real number substituted for \( x \) will result in 0.

8. Where can I find the next exercise solutions?

You can find the Exercise 2.3 solutions and chapter notes by clicking the navigation links at the bottom of this post.

Conclusion

We hope these NCERT Class 9 Maths Ganita Manjari Chapter 2 Exercise 2.2 solutions have helped you understand the practical applications of polynomials. From evaluating linear expressions to solving complex age and dimension word problems, these fundamentals are crucial for your exams.

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Last updated according to the latest NCERT Ganita Manjari syllabus.