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

Download free NCERT solutions for class 10 maths chapter 4 exercise 4.1 Quadratic Equations. Exercise 4.1 class 10 contains 2 questions, for which detailed answers have been provided in these solutions. Quadratic Equations Ex 4.1 class 10 Maths Chapter 4 NCERT Solutions have been explained in a simple and easy-to-understand language to help you learn and prepare for your upcoming class 10 Maths exams. Here we are sharing Quadratic Equations NCERT Solutions for class 10 chapter 4 Ex. 4.1.

Category	NCERT Solutions for Class 10
Subject	Maths
Chapter	Chapter 4
Exercise	Exercise 4.1
Chapter Name	Quadratic Equations

Download NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.1 Quadratic Equations

NCERT Solutions for Exercise 4.1 Class 10 Maths Quadratic Equations

1. Check whether the following are quadratic equations?

Solution: An equation of the form ax²+bx+c = 0, a ≠ 0 and a, b, c are real numbers is called quadratic equation.

(i) (x+1)² = 2(x-3)

x²+2x+1 = 2x-6
x²+2x+1 -2x+6 = 0
x²+7 = 0
Comparing above equation with ax²+bx+c = 0, we have a = 1≠ 0, b = 0, c = 7
Hence the given equation is quadratic equation.

(ii) x²-2x = (-2)(3-x)

x²-2x = -6+2x
x²-2x -2x+6 = 0
x²-4x+6 = 0
Comparing above equation with ax²+bx+c = 0, we have a = 1≠ 0, b = -4, c = 6
Hence the given equation is a quadratic equation.

(iii) (x-2)(x+1) = (x-1)(x+3)

x²-2x+x-2 = x²-x+3x-3
x²-2x+x-2 -x²+x-3x+3= 0
-3x+1 = 0
Comparing above equation with ax²+bx+c = 0, we have a = 0, b = -3, c = 1
Hence the given equation is not quadratic equation.

(iv) (x-3)(2x+1) = x(x+5)

x²-6x+x-3 = x²+5x
x²-6x+x-3 -x²-5x = 0
-10x-3 = 0
Comparing above equation with ax²+bx+c = 0, we have a = 0, b = -10, c = -3
Hence the given equation is not quadratic equation.

(v) (2x-1)(x-3) = (x+5)(x-1)

2x²-6x-x+3 = x²+5x-x-5
2x²-6x-x+3 -x²-5x+x+5 = 0
x²-11x+8 = 0
Comparing above equation with ax²+bx+c = 0, we have a = 1 ≠ 0, b = -11, c = 8
Hence the given equation is a quadratic equation.

(vi) x²+3x+1 = (x-2)²

x²+3x+1 = x²-4x+4
x²+3x+1 -x²+4x-4= 0
7x-3 = 0
Comparing above equation with ax²+bx+c = 0, we have a = 0, b = 7, c = -3
Hence the given equation is not quadratic equation.

(vii) (x+2)³ = 2x(x²-1)

x³+6x²+12x+8 = 2x³-2x
x³+6x²+12x+8 -2x³+2x = 0
x³– 6x²-14x-8 = 0
It is not in the form of ax²+bx+c = 0s
Hence the given equation is not a quadratic equation.

(viii) x³-4x²-x+1 = (x-2)³

x³-4x²-x+1 = x³-6x²+12x-8
x³-4x²-x+1 -x³+6x²-12x+8= 0
2x²-13x+9 = 0
Comparing above equation with ax²+bx+c = 0, we have a = 2 ≠ 0, b = -13, c = 9
Hence the given equation is a quadratic equation.

2. Represent the following situations in the form of quadratic equations:

(i) The area of the rectangular plot is 528 m². The length of the plot (in meters) is one more than twice its breadth. We need to find the length and breadth of the plot.

Solution: Let the breadth of the plot be x meters
Then, the length is (2x + 1) meters.
Area = length × breadth
528 = x × (2x + 1)
528 = 2x² + x
2x² + x – 528 = 0

(ii) The product of two consecutive positive integers is 306. We need to find the integers.

Solution: Let x and x+1 be two consecutive integers.
Then, x(x + 1) = 306
x²+ x – 306 = 0

(iii) Rohan’s mother is 26 years older than him. The products of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

Solution: Let x be the Rohan’s present age. Then, his mother’s present age is x+26
After 3 years theirs ages will be x+3 and x+26+3 = x+29 respectively.
Hence,
(x+3)(x+29) = 360
x²+3x+29x+87 = 360
x²+32x- 273 = 0

(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: Let the speed of the train be x km/h
Then it covers 480 km in (480/x) hours.
If the speed is x-8 km/hr then it takes (480/x-8) hours.
Hence, (480/x-8) – (480/x) = 3
[480(x-x+8)/x(x-8)] = 3
480×8 = 3x(x-8)
x²-8x = 160×8
x²– 8x -1280 = 0

Summary:

Exercise 4.1 class 10 in class 10 Maths contains 2 main question and these two questions have various sub questions. All the questions available in ex 4.1 class 10 have been explained accurately stepwise and the anwers have provided by the highly experienced subject experts in India. If you are a class 10 maths students and currntly preparing chapter 4 exercise 4.1 Quadratic Equations then you must be looking for the exercise 4.1 class 10 NCERT solutions. The NCERT class 10 maths text book contain all the questions but you mus visit Anrinjay Academy for the proper solutions. We have explained all the ex 4.1 class 10 questions above.

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