Question

Two friends Vicky and Love start a business together. They decided to share their capitals depending upon the variable

expenditure. The capital of the two

partners together is given by polynomial 6x+10x -35, which is the product of

their individual share factors.


On the basis of the above information,

answer the following questions.


i) The total expenditure of Vicky and Love

when x = 10 is (in )

(a) 375 (b) 475

(c) 575 (d) 675


(ii) The shares of the Vicky and Love

individually is

(a) 2x +7, 3x -

5

(b) 3x -5, 2x +7

(c) Both (a) and (b)

(d) None of the above


(iii) The value of x, when their shares are

equal

(a) 12 (b) 10

(c) 8 (d) 6


(iv) The value of x, when their total share is

equal tob0

7

(a)- (b) 3

(c) Both (a) and (b) (d) None of these


(v) The sum of their expenditure is

(a) 5r -2 (b)5x+2 (c) 4x-2 (d) 4x+2​

Answer 1

iAnswer:

i)    rs 675

ii)   both i and ii

iii)   12

iv)   both a and b

Step-by-step explanation:

Answer 2

Answers are:

1) 675

2) (2x+7)(3x-5) and vice versa.

3) 12

4) 5/3 and -3.5

5) 5x+2

Correct question:

Given:

• The capital of the two partners (Vicky and Love) together is given by polynomial 6x²+11x -35, which is the product of their individual share factors.

To find:

• (i) The total expenditure of Vicky and Love, when x = 10 is (in )

1. (a) 375
2. (b) 475
3. (c) 575
4. (d) 675

• (ii) The shares of the Vicky and Love individually is

1. (a) 2x +7, 3x -5
2. (b) 3x -5, 2x +7
3. (c) Both (a) and (b)
4. (d) None of the above

• (iii) The value of x, when their shares are equal

1. (a) 12
2. (b) 10
3. (c) 8
4. (d) 6

• (iv) The value of x, when their total share is equal to 0

1. (a)5/3
2. (b)- 3.5
3. (c) Both (a) and (b)
4. (d) None of these

• (v) The sum of their expenditure is

1. (a) 5x -2
2. (b)5x+2
3. (c) 4x-2
4. (d) 4x+2

Solution:

Part (I):

To find the total expenditure of Vicky and Love, when x= 10, put the value of x in expression.

Let$f(x) = 6 {x}^{2} + 11x - 35$

Put x=10

$f(10) = 6 {(10)}^{2} + 11(10) - 35$

$f(10) = 600 + 110- 35$

$\bf f(10) = 675$

Thus,

Option d is correct.

Part 2:

To find share of Vicky and Love individually, factorise the quadratic polynomial.

$6 {x}^{2} + 11x - 25$

$6 {x}^{2} + 21x - 10x - 35$

$= 3x(2x + 7) - 5(2x + 7)$

$\bf 6 {x}^{2} + 11x - 35 = (3x - 5)(2x + 7)$

Thus,

The individual share of Vicky and Love is (3x-5)(2x+7) respectively or vice versa.

Thus,

Option C is correct.

Part 3:

Find the value of x, when both shares are equal.

$3 x- 5 = 2x + 7$

$3x - 2x = 7 + 5$

$\bf x = 12$

Thus,

Option a is correct.

Part 4:

To find the value of x, when their total share is equal to zero.

$(3x - 5)(2x + 7) = 0$

$3x = 5$

$\bf x = \frac{5}{3}$

and

$2x + 7 = 0$

$2x = - 7$

$\bf x = - 3.5$

Thus,

Option c is correct.

Part 5:

To find the sum of their individual share add factors.

$= 3x - 5 + 2x + 7$

$\bf = 5x + 2$

Thus,

Option b is correct.

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