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## Andhra Pradesh State Board Class 10th Maths Chapter 5 Quadratic Equations Ex 5.1 Books Solutions

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### 10th Class Maths 5th Lesson Quadratic Equations Ex 5.1 Textbook Questions and Answers

Question 1.
Check whether the following are quadratic equations.
i) (x + l)2 = 2(x-3)
Given: (x + l)2 = 2(x – 3)
⇒ x2 + 2x + 1 = 2(x – 3) = 2x – 6
⇒ x2 + 2x + l – 2x + 6 = 0
⇒ x2 + 7 = 0 is a Q.E.

ii) x2 – 2x = (-2) (3 – x)
Given: x2 – 2x = -2(3 – x)
⇒ x2 – 2x = -6 + 2x
⇒ x2 – 4x + 6 = 0 is a Q.E.

iii) (x-2) (x + 1) = (x- 1) (x + 3)
Given: (x – 2) (x + 1) = (x – 1) (x + 3)
⇒ x (x + 1) – 2 (x +1)
= x (x + 3) – 1 (x + 3)
Note : Compare the coefficients of x2 on both sides. If they are equal it is not a Q.E.
⇒ x2 + x – 2x – 2 = x2 + 3x – x -3
⇒ x2 – x – 2 = x2 + 2x – 3
⇒ 3x – 1 = 0 is not a Q.E.

iv) (x – 3) (2x + 1) = x(x + 5)
Given: (x – 3) (2x + 1) = x(x + 5)
⇒ x (2x + 1) – 3 (2x + 1) = x . x + 5 . x
⇒ 2x2 + x – 6x – 3 = x2 + 5x
⇒ 2x2 – 5x – 3 – x2 – 5x = 0
⇒ x2 – 10x – 3 = 0 is a Q.E.
(or)
Comparing the coefficients of x2 on both sides.
x . 2x and x . x
⇒ 2x2 and x2
2x2 ≠ x2
Hence it’s a Q.E.

v) (2x – 1) (x – 3) = (x + 5) (x – 1)
Given: (2x – 1) (x – 3) = (x + 5) (x – 1)
⇒ 2x (x – 3) -1 (x – 3) = x (x – 1) + 5(x – 1)
⇒ 2x2 – 6x – x + 3 = x2 – x + 5x – 5
⇒ 2x2 -7x + 3 – x2 – 4x + 5 = 0
⇒ x2 – 11x + 8 = 0
Hence it’s a Q.E.
(or)
Co.eff. of x2 on L.H.S. = 2 × 1 = 2
Co.eff. of x2 on R.H.S = 1 × 1 = 1
LHS ≠ RHS Hence it is a Q.E.

vi) x2 + 3x + 1 = (x – 2)2
Given: x2 + 3x + 1 = (x – 2)2
⇒ x2 + 3x + 1 = x2 – 4x + 4
⇒ 7x – 3 = 0 is not a Q.E.

vii) (x + 2)3 = 2x (x2 – 1)
Given: (x + 2)3 = 2x(x2 – 1)
⇒ x3 + 6x2 + 12x + 8 = 2x3 – 2x [∵ (a + b)3 = a3 + 3a2b + 3ab2 + b3]
⇒ -x3 + 6x2 + 14x + 8 = 0
is not a Q.E. [∵ degree = 3]

viii) x3 – 4x2 – x + 1 = (x – 2)3
Given : x3 – 4x2 – x + 1 = (x – 2)3
⇒ x3 – 4x2 – x + 1 = x3 – 6x2 + 12x – 8
⇒ 6x2 – 12x + 8 – 4x2 – x + 1 = 0
⇒ 2x2 – 13x + 9 = 0 is a Q.E.

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 meters) is one more than twice its breadth. We need to find the length and breadth of the plot.
Let the breadth of the rectangular plot be x m.
Then its length (by problem) = 2x + 1.
Area = l . b = (2x + 1) . x = 2x2 + x
But area = 528 m2 (∵ given)
∴ 2x2 + x = 528
⇒ 2x2 + x – 528 = 0 where x is the breadth of the rectangle.

ii) The product of two consecutive positive integers is 306. We need to find the integers.
Let the consecutive integers be x and x + 1.
Their product = x(x + 1) = x2 + x
By problem x2 + x = 306
⇒ x2 + x – 306 = 0
where x is the smaller integer.

iii) Rohan’s mother is 26 years older than him. The product of their ages after 3 years will be 360 years. We need to find Rohan’s present age.
Let the present age of Rohan be x years.
Then age of Rohan’s mother = x + 26
After 3 years:
Age of Rohan would be = x + 3
Rohan’s mother’s age would be = (x + 26) + 3 = x + 29
By problem (x + 3) (x + 29) = 360
⇒ x(x + 29) + 3(x + 29) = 360
⇒ x2 + 29x + 3x + 87 = 360
⇒ x2 + 32x + 87 – 360 = 0
⇒ x2 + 32x – 273 = 0
⇒ x2 + 39x – 7x – 273 = 0
⇒ x (x + 39) – 7 (x + 39) = 0
⇒ (x – 7) (x + 39) = 0
⇒ x = 7 or x = -39 ‘x’ being age cannot be negative.
∴ x = Present age of Rohan = 7 years.

iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.
Let the speed of the train be x km/h.
Then time taken to travel a distance of distance of 480 km =  distance  speed  = 480𝑥
If the speed is 8km/h less, then time needed to cover the same distance would be 480𝑥−8

⇒ x2 – 8x = 1280
⇒ x2 – 8x – 1280 = 0
where x is the speed of the train.

## Andhra Pradesh Board Class 10th Maths Chapter 5 Quadratic Equations Ex 5.1 Textbooks for Exam Preparations

Andhra Pradesh Board Class 10th Maths Chapter 5 Quadratic Equations Ex 5.1 Textbook Solutions can be of great help in your Andhra Pradesh Board Class 10th Maths Chapter 5 Quadratic Equations Ex 5.1 exam preparation. The AP Board STD 10th Maths Chapter 5 Quadratic Equations Ex 5.1 Textbooks study material, used with the English medium textbooks, can help you complete the entire Class 10th Maths Chapter 5 Quadratic Equations Ex 5.1 Books State Board syllabus with maximum efficiency.

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