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

Complete solutions of Ex 4.1 Class 10 Maths Chapter 4 with additional questions and answers from new NCERT syllabus textbook Class 10 Maths.

NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.1 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.1.

    • Quadratic Equations Class 10 Ex 4.1
    • Quadratic Equations Class 10 Ex 4.2
    • Quadratic Equations Class 10 Ex 4.3
    • Quadratic Equations Class 10 Ex 4.4
Board CBSE
Textbook NCERT
Class Class 10
Subject Maths
Chapter Chapter 4
Chapter Name Quadratic Equations
Exercise Ex 4.1
Number of Questions Solved 2
Category NCERT Solutions

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:
(i) Given: (x+ 1)2=2(x-3)
⇒ x2 + 1 + 2x = 2x – 6
⇒ x2 + 1 + 2x – 2x + 1 = 0
⇒ x2 + 7 = 0
As the highest power of x is 2, so the given equation is quadratic.

(ii) Given: x2 – 2x = (- 2) (3 -x)
⇒ x2 -2x = -6 + 2x
⇒ x2 -4x + 6 = 0
As the highest power of x is 2, so the given equation is quadratic.

(iii) Given: (x – 2) (x + 1) = (x – 1) (x + 3)
⇒ x2  – 2x + x – 2 = x2 – x + 3x – 3
⇒ x2  – x – 2 = x2 + 2x – 3
⇒  3x – 1 = 0
As the highest power of x is 2, so the given equation is quadratic.

(iv) Given: (x-3) (2x+ 1) = x (x + 5)
⇒ 2x2  – 6x + x – 3 = x2 + 5x
⇒ x2 – 10x -3 = 0
As the highest power of x is 2, so the given equation is quadratic.

(v) Given: (2x-1)(x-3) = (x + 5)(x-1)
⇒ 2x2 – 6x – x + 3 = x2  + 5x – x – 5
⇒ x2 – 11x + 8 = 0
As the highest power of x is 2, so the given equation is quadratic..

(vi) Given: x2 + 3x + 1 = (x – 2)2
⇒ x2 + 3x + 1 = x2 + 4 – 4x
⇒ 7x – 3 = 0
As the highest power of x is 1, so the given equation is not quadratic.

(vii) Given: (x + 2)3 = 2x (x2 – 1)
⇒ x3 + 8 + 6x2 + 12x = 2x3 – 2x
⇒ x3 – 6x2 – 14x – 8 = 0
As the highest power of x is 1, so the given equation is not quadratic.

(viii) Given x3 – 4x2 – x+1 = (x – 2)3
⇒ x3 – 4x2 -x + 1 = x3 – 6x2 + 12x – 8
⇒ 2x2 – 13x + 9 = 0
As the highest power of x is 1, so the given equation is quadratic.

You can also Download NCERT Solutions for class 10 Maths in Hindi to help you to revise complete Syllabus and score more marks in your examinations.

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:
(i) Let breadth of the rectangular plot = x m
Then, length of the plot will be = (2x + 1)m
∴   x(2x + 1) = 528
⇒ 2x2 + x – 528 = 0
This is  required representation.

(ii) Let the two consecutive integers be x and x + 1 respectively.
Then, x(x + 1) = 306
⇒ x2 + x – 306 = 0
This is  required representation.

(iii) Let the present age of Rohan = x years
Then, his mother’s age will be = (x + 26) years
Three years from now:
Rohan’s age will be (x + 3) years.
His mother’s age will be = (x + 26 + 3)
= (x + 29) years
∴     (x + 3) (x + 29) = 360
⇒ x2 + 29x + 3x + 87 = 360
⇒ x2 + 32x + 87 – 360 = 0
⇒ x2 + 32x – 273 = 0
This is  required representation.

(iv)
Let speed of the train = x km/h
NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations 1

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