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.
| 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
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.
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
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