Master Class 10 Math Chapter 4 Quadratic Equations Ex 4.2

In Exercise 4.2 of Class 10 Mathematics, we focus on solving quadratic equations using the factorization method. This method involves expressing a quadratic equation as a product of two linear factors and finding the roots by setting each factor equal to zero.

The general form of the quadratic equation we work with is:
ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0

By factorizing these equations, we can find the values of x, also known as the roots of the equation. The factorization method is based on splitting the middle term into two terms, which allows us to group and simplify the equation.

In this exercise, we will apply the factorization method to different types of quadratic equations and find their solutions. Let’s get started!

Class 10 Math Chapter 4 Quadratic Equations Ex 4.2

Question 1.
Find the roots of the following quadratic equations by factorisation:
(i) x² -3x – 10 = 0
(ii) 2x² + x – 6 = 0
(iii) √2x² + 7x + 5√2 = 0
(iv) 2x² – x + [Math Processing Error] = 0 8
(v) 100 x² – 20 X + 1 = 0
Solution:
NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Exercise 4.2 Q1

Question 2.
Solve the following situations mathematically:
(i) John and Jivanti together have 45 marbles. Both of them lost 5 marbles each and the product of the number of 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 ₹750. We would like to find out the number of toys produced on that day.
Solution:
Exercise 4.2 Class 10 Maths NCERT Solutions Chapter 4 Quadratic Equations PDF Download Q2

Question 3.
Find two numbers whose sum is 27 and product is 182.
Solution:
Exercise 4.2 Class 10 Maths NCERT Solutions Chapter 4 Quadratic Equations Free PDF Download Q3

Ex 4.2 Class 10 Maths Question 4.
Find two consecutive positive integers, the sum of whose squares is 365.
Solution:
Exercise 4.2 Class 10 Maths NCERT Solutions Chapter 4 Quadratic Equations PDF Q3

Ex 4.2 Class 10 Maths

Question 5.
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
Solution:
Exercise 4.2 Class 10 Maths NCERT Solutions Chapter 4 Quadratic Equations Q5

Question 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 ₹90, find the number of articles produced and the cost of each article.
Solution:
Chapter 4 Maths Class 10 NCERT Solutions Exercise 4.2 PDF Download Q6