NCERT Solutions For Class 10 Maths Chapter 4 Quadratic Equations

NCERT Solutions For Class 10 Maths Chapter 4 Quadratic Equations

NCERT Solutions For Class 10 Maths Chapter 4 Quadratic Equations Ex 4.1

Ex 4.1 Class 10 Maths Question 1.

Check whether the following are quadratic equations:
(i) (x+ 1)2=2(x-3)
(ii) x – 2x = (- 2) (3-x)
(iii) (x – 2) (x + 1) = (x – 1) (x + 3)
(iv) (x – 3) (2x + 1) = x (x + 5)
(v) (2x – 1) (x – 3) = (x + 5) (x – 1)
(vi) x2 + 3x + 1 = (x – 2)2
(vii) (x + 2)3 = 2x(x2 – 1)
(viii) x3 -4x2 -x + 1 = (x-2)3
Solution:

NCERT Solutions Class 10 Maths chapter 4 Quadratic Equations- Video

You can also watch the video solutions of NCERT Class10 Maths chapter 4 Quadratic Equations here.

Ex 4.1 Class 10 Maths Question 2.

Represent the following situations in the form of quadratic equations:
(i) The area of a rectangular plot is 528 m2. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.
(ii) The product of two consecutive positive integers is 306. We need to find the integers.
(iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.
(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.
Solution:

NCERT Solutions For Class 10 Maths Chapter 4 Quadratic Equations Ex 4.2

Ex 4.2 Class 10 Maths 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 +  = 0 8
(v) 100 x2 – 20 X + 1 = 0
Solution:

Ex 4.2 Class 10 Maths 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:

Ex 4.2 Class 10 Maths Question 3.
Find two numbers whose sum is 27 and product is 182.
Solution:

Ex 4.2 Class 10 Maths Question 4.
Find two consecutive positive integers, the sum of whose squares is 365.
Solution:

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:

Ex 4.2 Class 10 Maths 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:

NCERT Solutions For Class 10 Maths Chapter 4 Quadratic Equations Ex 4.3

Ex 4.3 Class 10 Maths Question 1.
Find the roots of the following quadratic equations, if they exist, by the method of completing the square:
(i) 2x2 – 7x + 3 = 0
(ii) 2x2 + x – 4 = 0
(iii) 4x2 + 4√3x + 3 = 0
(iv) 2x2 + x + 4 = 0
Solution:

Ex 4.3 Class 10 Maths Question 2.

Find the roots of the quadratic equations by applying the quadratic formula.
(i) 2x2 – 7x + 3 = 0
(ii) 2x2 – x + 4 = 0
(iii) 4x2 – 4√3x + 3 = 0
(iv) 2x2 – x + 4 = 0
Solution:

Ex 4.3 Class 10 Maths Question 3.
Find the roots of the following equations:


Solution:

Ex 4.3 Class 10 Maths Question 4.
The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is  Find his present age.
Solution:

Ex 4.3 Class 10 Maths Question 5.
In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.
Solution:

Ex 4.3 Class 10 Maths Question 6.
The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.
Solution:

Ex 4.3 Class 10 Maths Question 7.
The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.
Solution:

Ex 4.3 Class 10 Maths Question 8.
A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
Solution:

Ex 4.3 Class 10 Maths Question 9.
Two water taps together can fill a tank in 9 hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
Solution:

Ex 4.3 Class 10 Maths Question 10.
An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bengaluru (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11 km/h more than that of the passenger train, find the average speed of the two trains.
Solution:

Ex 4.3 Class 10 Maths Question 11.
Sum of the areas of two squares is 468 m2. If the difference of their perimeters is 24 m, find the sides of the two squares.
Solution:

NCERT Solutions For Class 10 Maths Chapter 4 Quadratic Equations Ex 4.4

Ex 4.4 Class 10 Maths Question 1.
Find the nature of the roots of the following quadratic equations. If the real roots exist, find them:
(i) 2x² -3x + 5 = 0
(ii) 3x2 – 4√3x + 4 = 0
(iii) 2x2-6x + 3 = 0
Solution:

Ex 4.4 Class 10 Maths Question 2.

Find the values of k for each of the following quadratic equations, so that they have two equal roots.
(1) 2x2 + kx + 3 = 0
(2) kx (x – 2) + 6 = 0
Solution:

Ex 4.4 Class 10 Maths Question 3.
Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m2? If so, find its length and breadth.
Solution:

Ex 4.4 Class 10 Maths Question 4.
Is the following situation possible? If so, determine their present ages.
The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Solution:

Ex 4.4 Class 10 Maths Question 5.
Is it possible to design a rectangular park of perimeter 80 m and area 400 m2? If so, find its length and breadth.
Solution:

Quadratic Equations Class 10 Extra Questions Maths Chapter 4

Extra Questions for Class 10 Maths Chapter 4 Quadratic Equations. According to new CBSE Exam Pattern, MCQ Questions for Class 10 Maths Carries 20 Marks.

You can also download Class 10 Maths to help you to revise complete syllabus and score more marks in your examinations.

Quadratic Equations CBSE Class 10 Extra Questions Q2: