Solutions of Cbse Ncert Mathematics
CBSE Board - Class X, Mathematics (SA-II / Term II)
Chapter 4, Quadratic EquationS
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, x2 – 3x – 10 = 0
=> x2 + 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, 2x2 + x – 6 = 0
=> 2x2 + 4x – 3x – 6 = 0
=> 2x(x + 2) – 3(x + 2) = 0
=> (x + 2) (2x – 3) = 0
Hence, the roots of this equation are,
.JPG "CBSE Class 10 Math Solutions, Quadratic Equations")
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 – x2 –200
+ 5x = 124
=> –x2 + 45x –
324 = 0
=> –x2 + 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 – x2 =
182
=> –x2 + 27x –
182 = 0
=> –x2 + 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,
x2 + (x + 1)2
= 365
=> 2x2 + 2x –
364 = 0
=> x2 + x – 182
= 0
=> x2 – 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 + x2
=> 169 =
(x2 – 14x + 49) + x2
=> 2x2
– 14x – 120 = 0
=> x2
– 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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