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**Solutions of Cbse
Ncert Mathematics**

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**CBSE Board - Class X,
Mathematics (SA-II / Term II) **

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*Chapter 4, Quadratic EquationS *

*Chapter 4, Quadratic EquationS*

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__NCERT Solutions
for Mathematics Textbook Exercise 4.2__

__NCERT Solutions for Mathematics Textbook Exercise 4.2__

*(NCERT Math Textbook Page 76)*

**1: Find the roots of the following quadratic equations by factorization:**

__Solution.1(i)__:

We have, x

^{2}– 3x – 10 = 0
=> x

^{2}+ 2x – 5x – 10 = 0
=> x(x + 2) – 5(x + 2) = 0

=> (x + 2) (x – 5) = 0

Hence, the roots of this equation are,

(x + 2) = 0

or, x = –2 and

(x – 5) = 0

or, x = 5

or, x = –2, 5

__Solution.1(ii)__:

We have, 2x

^{2}+ x – 6 = 0
=> 2x

^{2}+ 4x – 3x – 6 = 0
=> 2x(x + 2) – 3(x + 2) = 0

=> (x + 2) (2x – 3) = 0

Hence, the roots of this equation are,

__Solution.1(iii)__:

__Solution.1(iv)__:

__Solution.1(v)__: Taking hint from the above solve it yourself.

**2: Represent the following situations mathematically:**

**(i) Jhon and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of the marbles they now have is 124. We would like to find out how many marbles they had to start with.**

**(ii) A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. We would like to find out the number of toys produced on that day.**

__Solution.2(i)__:

Let the number of marbles John
had = x.

Then the number of marbles
Jivanti had = (45 – x)

After losing 5 marbles by each
of them, John has (x – 5) marbles and Jivanti has (40 – x) marbles.

As per the given condition,

(x – 5) (40 – x) = 124

=> x(40 – x) – 5(40 – x) =
124

=> 40x – x

^{2}–200 + 5x = 124
=> –x

^{2}+ 45x – 324 = 0
=> –x

^{2}+ 36x + 9x – 324 = 0
=> (x – 36) (–x + 9) = 0

or, x = 36 and 9.

Therefore, the number of
marbles John had is 36 and the number of marbles Jivanti had is

(45 – 9) i.e.
9. And if the number with John is 9,
then it will be 36 with Jivanti.

__Solution.2(ii)__: Taking hint from 2(i) solution, try to solve it yourself.

**3: Find two numbers whose sum is 27 and product is 182.**

__Solution.3__: Let the first number be ‘x’ and the other number will be (27 – x).

As per the given condition,

x(27 – x) = 182

=> 27x – x

^{2}= 182
=> –x

^{2 }+ 27x – 182 = 0
=> –x

^{2 }+ 14x + 13x – 182 = 0
=> –x(x – 14) + 13(x – 14)
= 0

=> (13 – x) (x – 14) = 0

Hence, one number is 13 and
the other number is (27 – 13) = 14.

**4: Find two consecutive positive integers, sum of whose squares is 365.**

__Solution.4__: Let the first positive integer be ‘x’ and the second positive integer will be then (x + 1). As per the given condition,

x

^{2}+ (x + 1)^{2}= 365
=> 2x

^{2}+ 2x – 364 = 0
=> x

^{2}+ x – 182 = 0
=> x

^{2}– 13x + 14x – 182 = 0
=> x(x – 13) + 14(x – 13) =
0

=> (x + 14) (x – 13) = 0

or, x = 13 and –14.

Since, ‘x’ is the positive
integer so it can not be –14. Hence, first positive integer is 13 and the
second positive integer is (13 + 1) i.e. 14.

**5: The altitude of a right triangle is 7cm less than its base. If the hypotenuse is 13 cm, find the other two sides.**

__Solution.5__:

(13)

^{2}= (x – 7)^{2}+ x^{2}
=> 169 =
(x

^{2}– 14x + 49) + x^{2 }
=> 2x

^{2 }– 14x – 120 = 0
=> x

^{2 }– 7x – 60 = 0
=> (x –
12) (x + 5) = 0

or, x = 12
and –5.

Since ‘x’ is
base (one side) of a triangle, so it can not be negative. Hence, base is 12 cm
and the other side (altitude) is (12 – 7) i.e. 5 cm.

**6: A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.**

**Hint**

**to solve**- Let the number of articles produced be ‘x’ and the cost of production of each article on that day (3 + 2x). Now as per the given condition, x(3 + 2x) = 90. Also, remember since ‘x’ is the number of the articles produced and so it can not be a negative number.

At the end of completing all Exercises from
each Chapter given in

*NCERT Math textbook*, we shall provide**CBSE Notes (Hints) / important Solutions of CBSE Questions, Mathematics Sample Questions**with their Solutions and many more…
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