Exercise 4.1 (NCERT) – Quadratic Equations, Class 10
| Chapter 4 | Exercise 4.1 | Class 10 |
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Below are the Quick links for all questions of Exercise 4.1, Quadratic Equations, Class 10. Click a link to view the solution of corresponding question.
Below are the solutions of every question of exercise 4.1 of chapter 4, Quadratic Equations, NCERT of class 10. YouTube video tutorial of every question is also embedded along with the written solution.
Question 1
Check whether the following are quadratic equations :
(i) (x + 1)2 = 2(x – 3)
Expand the equation
This is in the form ax2 + bx + c = 0 where a = 1, b = 0, c = 7
Answer: Yes, it is a Quadratic Equation.
(ii) x2 – 2x = (–2) (3 – x)
This is in the form ax2 + bx + c = 0 where a = 1, b = -4, c = 6
Answer: Yes, it is a Quadratic Equation.
(iii) (x – 2)(x + 1) = (x – 1)(x + 3)
This is not in the form ax2 + bx + c = 0 because its highest degree is 1.
Answer: No, it is not a Quadratic Equation.
(iv) (x – 3)(2x +1) = x(x + 5)
This is in the form ax2 + bx + c = 0 where a = 1, b = -10, c = -3
Answer: Yes, it is a Quadratic Equation.
(v) (2x – 1)(x – 3) = (x + 5)(x – 1)
This is in the form ax2 + bx + c = 0 where a = 1, b = -11, c = 8
Answer: Yes, it is a Quadratic Equation.
(vi) x2 + 3x + 1 = (x – 2)2
This is not in the form ax2 + bx + c = 0 because its highest degree is 1.
Answer: No, it is not a Quadratic Equation.
(vii) (x + 2)3 = 2x (x2 – 1)
This is not in the form ax2 + bx + c = 0 because its highest degree is 3.
Answer: No, it is not a Quadratic Equation.
(viii) x3 – 4x2– x + 1 = (x – 2)3
This is in the form ax2 + bx + c = 0 where a = 2, b = -13, c = 9
Answer: Yes, it is a Quadratic Equation.
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.
Let the breadth be x metres
Then, length = 2x + 1 metres
Area = length × breadth = 528
⇒ (2x + 1)(x) = 528
⇒ 2x2 + x = 528
⇒ 2x2 + x − 528 = 0
Answer: 2x2 + x − 528 = 0
(ii) The product of two consecutive positive integers is 306. We need to find the integers.
Let the smaller integer be x
Then the next integer = x + 1
Given: Product of numbers = 306
⇒ x(x + 1) = 306
⇒ x2 + x = 306
⇒ x2 + x − 306 = 0
Answer: x2 + x − 306 = 0
(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.
Let Rohan’s present age be x years
Then his mother’s present age = x + 26 years
After 3 years:
Rohan’s age = x + 3
Mother’s age = x + 26 + 3 = x + 29
Given: Product of their ages = 360
⇒ (x + 3)(x + 29) = 360
⇒ x2 + 32x + 87 = 360
⇒ x2 + 32x − 273 = 0
Answer: 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.
Case 1: Normal Speed
Let the train’s speed be x km/h
Case 2: Slower Speed
Speed = x – 8 km/h
Time taken at slower speed = 3 Hours more than normal speed
Answer: x2 − 8x − 1280 = 0