Introduction to Linear Polynomials Mathematics Ganita Manjari class 9 in English Medium ncert book solutions Exercise Set 2.2

 

Q1. Find the value of the linear polynomial 5x – 3 if:
(i) x = 0 (ii) x = –1 (iii) x = 2

Solutions: 

P(x) = 5x - 3 

(i) x = 0 

P(0) = 5(0) - 3 

        = 0 - 3 

        = - 3 Ans 

(ii) x = -1 

P(-1) = 5(-1) - 3 

        = -5 - 3 

        = - 8 Ans 

(iii) x = 2 

P(2) = 5(2) - 3 

        = 10 - 3 

        = 7 Ans 

Q2. Find the value of the quadratic polynomial 7s² – 4s + 6 if:
(i) s = 0 (ii) s = –3 (iii) s = 4

Solution: 

P(s) = 7s² - 4s + 6 

(i) s = 0 

P(0) = 7(0)² - 4(0) + 6 

        = 0 - 0 + 6 

        = 6 Ans

(ii) s = –3 

P(–3) = 7(–3)² - 4(–3) + 6 

        = 63 + 12 + 6 

        = 81 Ans

(iii) s = 4 

P(4) = 7(4)² - 4(4) + 6 

        = 112 - 16 + 6 

        = 118 - 16 

        = 102 Ans

Q3. 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 the Salil's present Age be x 

Salil's Mother present age = 3x 

After 5 years

Salil's age = x + 5 

Salil's mother age = 3x + 5 

So, 

Therefore, Salil's Present Age = 15 years 

Salil's Mother Present Age = 3 x 15 = 45 years

Q4. The difference between two positive integers is 63. The ratio of the two integers is 2:5. Find the two integers.

Solution: 

Ratio of the two integers = 2 : 5 

Let the first integer be 2x 

And the second integer be 5x 

So, 5x - 2x = 63 

3x = 63 

x = 63/3 

x = 21 

The first integer = 2 x 21 = 42

The second integer = 5 x 21 = 105 

Q5. 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 the number of five-rupee coins be x.

Then, the number of two-rupee coins will be 3x.

Value of five-rupee coins = 5x

Value of two-rupee coins = 2(3x)

According to the question:

5x + 2(3x) = 88

Now solve:

5x + 6x = 88

11x = 88

x = 88/11

x = 8

So, number of five-rupee coins = 8

Number of two-rupee coins = 3 × 8 = 24

Therefore:

Five-rupee coins = 8

Two-rupee coins = 24

Q6. 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 length of the shorter piece be x feet.

Then, the length of the longer piece will be 4x feet.

According to the question:

x + 4x = 300

Now solve:

5x = 300

x = 300/5

x = 60

So, length of the shorter piece = 60 feet

Length of the longer piece = 4 × 60

= 240 feet

Therefore:

Shorter piece = 60 feet

Longer piece = 240 feet

Q7. 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 the width of the rectangle be x cm.

Then, the length of the rectangle will be 2x + 3 cm.

Perimeter of rectangle = 2(length + width)

According to the question:

2[(2x + 3) + x] = 24

Now solve:

2(3x + 3) = 24

6x + 6 = 24

6x = 24 − 6

6x = 18

x = 18/6

x = 3

So, width of the rectangle = 3 cm

Length of the rectangle = 2(3) + 3

= 6 + 3

= 9 cm

Therefore:

Width = 3 cm

Length = 9 cm

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