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AP Board Class 10 Maths Chapter 5 Quadratic Equations Ex 5.4 Textbook Solutions PDF: Download Andhra Pradesh Board STD 10th Maths Chapter 5 Quadratic Equations Ex 5.4 Book Answers

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Andhra Pradesh Board Class 10th Maths Chapter 5 Quadratic Equations Ex 5.4 Textbooks Solutions PDF

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Andhra Pradesh State Board Class 10th Maths Chapter 5 Quadratic Equations Ex 5.4 Books Solutions

Board	AP Board
Materials	Textbook Solutions/Guide
Format	DOC/PDF
Class	10th
Subject	Maths
Chapters	Maths Chapter 5 Quadratic Equations Ex 5.4
Provider	Hsslive

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10th Class Maths 5th Lesson Quadratic Equations Ex 5.4 Textbook Questions and Answers

Question 1.
Find the nature of the roots of the following quadratic equations. If real roots exist, find them.
i) 2x² – 3x + 5 = 0
Answer:
Given: 2x² – 3x + 5 = 0
a = 2; b = -3; c = 5
Discriminant = b² – 4ac
b² – 4ac = (-3)² – 4(2)(5)
= 9 – 40
= -31 < 0
∴ Roots are imaginary.

ii) 3x² – 4√3x + 4 = 0
Answer:
Given: 3x² – 4√3x + 4 = 0
a = 3; b = -4√3; c = 4
b² – 4ac = (-4√3)² – 4(3)(4)
= 48 – 48 = 0
∴ Roots are real and equal and they
−𝑏2𝑎, −𝑏2𝑎

iii) 2x² – 6x + 3 = 0
Answer:
Given: 2x² – 6x + 3 = 0
a = 2; b = -6; c = 3
b² – 4ac = (-6)² – 4(2)(3)
= 36 – 24
= 12 > 0
∴ The roots are real and distinct. They are

Question 2.
Find the values of k for each of the fol-lowing quadratic equations so that they have two equal roots.
i) 2x² + kx + 3 = 0
Answer:
Given : 2x² + kx + 3 = 0 has equal roots
∴ b² – 4ac = 0
Here a = 2; b = k; c = 3
b² – 4ac = (k)² – 4(2)(3) = 0
⇒ k² – 24 = 0
⇒ k² = 24
⇒ k = √24 = ± 2√6

ii) kx(x – 2) + 6 = 0
Answer:
Given: kx(x – 2) + 6 = 0
kx² – 2kx + 6 = 0
As this Q.E. has equal roots,
b² – 4ac = 0
Here
a = k; b = -2k; c = 6
∴ b² – 4ac = (-2k)² – 4(k)(6) = 0
⇒ 4k² – 24k = 0
⇒ 4k(k – 6) = 0
⇒ 4k = 0 (or) k – 6 = 0
⇒ k = 0 (or) 6
But k = 0 is trivial
∴ k = 6.

Question 3.
Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m²? If so, find its length and breadth.
Answer:
Let the breadth = x m
Then length = 2x m
Area = length x breadth = x.(2x)
= 2x² m²
By problem 2x² = 800 ⇒ x² = 400
and x = √400 = ± 20
∴ Breadth x = 20 m and
length 2x = 2 × 20 = 40 m.

Question 4.
The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48. Is the above situation possible? If so, deter¬mine their present ages.
Answer:
Let the age one of the two friends be x years.
Then the age of the other = 20 – x
Then, 4 years ago their ages would be (x – 4) and (20 – x – 4) = 16 – x
∴ Product of their ages 4 years ago = (x – 4) (16 – x)
By problem (x – 4) (16 – x) = 48
⇒ x(16 – x) – 4(16 – x) = 48
⇒ 16x – x² – 64 + 4x = 48
⇒ x² – 20x + 112 = 0
Here a = 1; b = -20; c = 112
b² – 4ac = (-20)² – 4(1) (112)
= 400 – 448
= -48 < 0
Thus the roots are not real.
∴ The situation is not possible.

Question 5.
Is it possible to design a rectangular park of perimeter 80 m and area 400 m²? If so, find its length and breadth.
Answer:
Given: Perimeter of a rectangle 2(1 + b) = 80
⇒ 6 + b = 802 = 40
Area of the rectangle, l × b = 400
If possible, let us suppose that length of the rectangle = x m say
Then its breadth by equation (1) = 40 – x
By problem area = x . (40 – x) = 400
⇒ 40x – x² = 400
⇒ x² – 40x + 400 = 0
Here a = 1; b = -40; c = +400
b² – 4ac = (-40)² – 4(1)(+400)
= 1600 – 1600 = 0
∴ The roots are real and equal.
They are −𝑏2𝑎, −𝑏2𝑎
i.e., −(−40)2×1 = 402 = 20
∴ The dimensions are 20 m, 20 m.
(∴ The park is in square shape)

AP Board Textbook Solutions PDF for Class 10th Maths

AP Board Class 10 Maths Chapter 1 Real Numbers Textbook Solutions PDF

AP Board Class 10 Maths Chapter 2 Sets Textbook Solutions PDF

AP Board Class 10 Maths Chapter 3 Polynomials Textbook Solutions PDF

AP Board Class 10 Maths Chapter 4 Pair of Linear Equations in Two Variables Textbook Solutions PDF

AP Board Class 10 Maths Chapter 5 Quadratic Equations Textbook Solutions PDF

AP Board Class 10 Maths Chapter 6 Progressions Textbook Solutions PDF

AP Board Class 10 Maths Chapter 7 Coordinate Geometry Textbook Solutions PDF

AP Board Class 10 Maths Chapter 8 Similar Triangles Textbook Solutions PDF

AP Board Class 10 Maths Chapter 9 Tangents and Secants to a Circle Textbook Solutions PDF

AP Board Class 10 Maths Chapter 10 Mensuration Textbook Solutions PDF

AP Board Class 10 Maths Chapter 11 Trigonometry Textbook Solutions PDF

AP Board Class 10 Maths Chapter 12 Applications of Trigonometry Textbook Solutions PDF

AP Board Class 10 Maths Chapter 13 Probability Textbook Solutions PDF

AP Board Class 10 Maths Chapter 14 Statistics Textbook Solutions PDF

Andhra Pradesh Board Class 10th Maths Chapter 5 Quadratic Equations Ex 5.4 Textbooks for Exam Preparations

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