EXERCISE 4.2 — NCERT Solutions for Class 10 Mathematics Chapter 4

EXERCISE 4.2 1–6 (part 2 of 3)

Exercise 1
Find the roots of the following quadratic equations by factorisation:
(i)
$\displaystyle x^{2}-3 x-10=0$
(ii)
$\displaystyle 2 x^{2}+x-6=0$
(iii)
$\displaystyle \sqrt{2} x^{2}+7 x+5 \sqrt{2}=0$
(iv)
$\displaystyle 2 x^{2}-x+\frac{1}{8}=0$
(v)
$\displaystyle 100 x^{2}-20 x+1=0$
NCERT’s answer
(i)
-$\displaystyle 2,5$ (ii) $\displaystyle -2, \frac{3}{2}$ (iii) $\displaystyle -\frac{5}{\sqrt{2}},-\sqrt{2}$ (iv) $\displaystyle \frac{1}{4}, \frac{1}{4}$ (v) $\displaystyle \frac{1}{10}, \frac{1}{10}$
Working being prepared
Exercise 2
Solve the problems given in Example 1.
NCERT’s answer
(i)
$\displaystyle 9,36$ (ii) $\displaystyle 25,30$
Working being prepared
Exercise 3
Find two numbers whose sum is $\displaystyle 27$ and product is 182.
NCERT’s answer
Numbers are $\displaystyle 13$ and 14.
Working being prepared
Exercise 4
Find two consecutive positive integers, sum of whose squares is 365.
NCERT’s answer
Positive integers are $\displaystyle 13$ and 14.
Working being prepared
Exercise 5
The altitude of a right triangle is $\displaystyle 7$ cm less than its base. If the hypotenuse is $\displaystyle 13$ cm, find the other two sides.
NCERT’s answer
$\displaystyle 5$ cm and $\displaystyle 12$ cm
Working being prepared
Exercise 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 $\displaystyle 3$ more than twice the number of articles produced on that day. If the total cost of production on that day was ₹ $\displaystyle 90$ , find the number of articles produced and the cost of each article.
NCERT’s answer
Number of articles $\displaystyle =6$, Cost of each article $\displaystyle =₹ 15$
Working being prepared

EXERCISE 4.2 1–6 (part 2 of 3)

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6