Exercise Set 2.2 Class 9 · Ganita Manjari
📘 Chapter 2 — Polynomials
📌 Complete Solutions
📐
Evaluating polynomials means substituting the given value of the variable into the polynomial.
Word problems can be solved by forming linear equations from the given conditions.
1
Find the value of the linear polynomial 5x − 3 if:
(i) x = 0
(ii) x = −1
(iii) x = 2
(i) x = 0
(ii) x = −1
(iii) x = 2
Given polynomial: 5x − 3
(i)
x = 0
= 5(0) − 3
= −3
= −3
(ii)
x = −1
= 5(−1) − 3
= −5 − 3
= −8
= −5 − 3
= −8
(iii)
x = 2
= 5(2) − 3
= 10 − 3
= 7
= 10 − 3
= 7
2
Find the value of the quadratic polynomial 7s² − 4s + 6 if:
(i) s = 0
(ii) s = −3
(iii) s = 4
(i) s = 0
(ii) s = −3
(iii) s = 4
(i)
s = 0
7s² − 4s + 6
= 7(0)² − 4(0) + 6
= 6
= 7(0)² − 4(0) + 6
= 6
(ii)
s = −3
7s² − 4s + 6
= 7(−3)² − 4(−3) + 6
= 7(9) + 12 + 6
= 63 + 12 + 6
= 81
= 7(−3)² − 4(−3) + 6
= 7(9) + 12 + 6
= 63 + 12 + 6
= 81
(iii)
s = 4
7s² − 4s + 6
= 7(4)² − 4(4) + 6
= 7(16) − 16 + 6
= 112 − 16 + 6
= 102
= 7(4)² − 4(4) + 6
= 7(16) − 16 + 6
= 112 − 16 + 6
= 102
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.
Let Salil’s present age = x years
Mother’s present age = 3x years
After 5 years:
- Salil’s age = x + 5
- Mother’s age = 3x + 5
According to question:
(x + 5) + (3x + 5) = 70
⇒ 4x + 10 = 70
⇒ 4x = 60
⇒ x = 15
⇒ 4x + 10 = 70
⇒ 4x = 60
⇒ x = 15
✅
Therefore, Salil’s age = 15 years
Mother’s age = 45 years
Mother’s age = 45 years
4
The difference between two positive integers is 63. The ratio of the two integers is 2:5. Find the two integers.
Let the integers be 2x and 5x
Difference:
5x − 2x = 63
⇒ 3x = 63
⇒ x = 21
⇒ 3x = 63
⇒ x = 21
Integers:
- 2x = 42
- 5x = 105
✅
Required integers are 42 and 105.
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?
Let number of five-rupee coins = x
Number of two-rupee coins = 3x
Total value:
5x + 2(3x) = 88
⇒ 5x + 6x = 88
⇒ 11x = 88
⇒ x = 8
⇒ 5x + 6x = 88
⇒ 11x = 88
⇒ x = 8
✅
Hence:
Five-rupee coins = 8
Two-rupee coins = 24
Five-rupee coins = 8
Two-rupee coins = 24
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?
Let shorter piece = x feet
Longer piece = 4x feet
Total:
x + 4x = 300
⇒ 5x = 300
⇒ x = 60
⇒ 5x = 300
⇒ x = 60
✅
Therefore:
Shorter piece = 60 feet
Longer piece = 240 feet
Shorter piece = 60 feet
Longer piece = 240 feet
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?
Let width = x cm
Length = 2x + 3 cm
Perimeter = 2(length + width)
2[(2x + 3) + x] = 24
⇒ 2(3x + 3) = 24
⇒ 6x + 6 = 24
⇒ 6x = 18
⇒ x = 3
⇒ 2(3x + 3) = 24
⇒ 6x + 6 = 24
⇒ 6x = 18
⇒ x = 3
✅
Therefore:
Width = 3 cm
Length = 2(3) + 3 = 9 cm
Width = 3 cm
Length = 2(3) + 3 = 9 cm