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NCERT Solutions for Exercise 4.2 Class 10 Maths Chapter 4 - Quadratic Equations

NCERT Solutions for Exercise 4.2 Class 10 Maths Chapter 4 - Quadratic Equations

Edited By Ramraj Saini | Updated on Nov 16, 2023 11:42 AM IST | #CBSE Class 10th

NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2

NCERT Solutions for Exercise 4.2 Class 10 Maths Chapter 4 Quadratic Equations are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. This ex 4.2 class 10 deals with the concept of solution of the quadratic equation by factorization. The general form of the quadratic equation in the variable x is ax2+ bx + c = 0 where a, b, c are real numbers. Class 10 maths ex 4.2 comprises 6 straightforward questions with sub-questions that are simple to illuminate and additionally explore the concepts and nature of the roots. In exercise 4.2 Class 10 Maths, there are three main methods to solve the quadratic equation i.e. Factorizations, Completing the square and Quadratic Formula.

This Story also Contains
  1. NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2
  2. Download Free Pdf of NCERT Solutions for Class 10 Maths chapter 4 exercise 4.2
  3. Assess NCERT Solutions for Class 10 Maths chapter 4 exercise 4.2
  4. More About NCERT Solutions for Class 10 Maths Exercise 4.2: Quadratic Equations
  5. Benefits of NCERT Solutions for Class 10 Maths Exercise 4.2:
  6. NCERT Solutions of Class 10 Subject Wise
  7. Subject Wise NCERT Exemplar Solutions
NCERT Solutions for Exercise 4.2 Class 10 Maths Chapter 4 - Quadratic Equations
NCERT Solutions for Exercise 4.2 Class 10 Maths Chapter 4 - Quadratic Equations

NCERT solutions for Class 10 Maths exercise 4.2, focused on the concepts of solving quadratic equations and understanding more about the relationship between the roots of the equation and the nature of the equation. These class 10 maths ex 4.2 solutions are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.

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Quadratic Equations class 10 chapter 4 Excercise: 4.2

Q1 (i) Find the roots of the following quadratic equations by factorization: x^2 - 3x - 10 =0

Answer:

Given the quadratic equation: x^2 - 3x - 10 =0

Factorization gives, x^2 - 5x+2x - 10 =0

\Rightarrow x^2 - 5x+2x - 10 =0

\Rightarrow x(x-5) +2(x-5) =0

\Rightarrow (x-5)(x+2) =0

\Rightarrow x= 5\ or\ -2

Hence, the roots of the given quadratic equation are 5\ and\ -2 .

Q1 (ii) Find the roots of the following quadratic equations by factorization: 2x^2 + x - 6 = 0

Answer:

Given the quadratic equation: 2x^2 + x - 6 = 0

Factorisation gives, 2x^2 +4x-3x - 6 = 0

\Rightarrow 2x(x+2) -3(x+2) =0

\Rightarrow (x+2)(2x-3) = 0

\Rightarrow x= -2\ or\ \frac{3}{2}

Hence, the roots of the given quadratic equation are

-2\ and\ \frac{3}{2}

Q1 (iii) Find the roots of the following quadratic equations by factorization: \sqrt2x^2 + 7x + 5\sqrt2 = 0

Answer:

Given the quadratic equation: \sqrt2x^2 + 7x + 5\sqrt2 = 0

Factorization gives, \sqrt2x^2 + 5x+2x + 5\sqrt2 = 0

\Rightarrow x(\sqrt2 x +5) +\sqrt2 (\sqrt 2 x +5)= 0

\Rightarrow (\sqrt2 x +5)(x+\sqrt{2}) = 0

\Rightarrow x=\frac{-5}{\sqrt 2 }\ or\ -\sqrt 2

Hence, the roots of the given quadratic equation are

\frac{-5}{\sqrt 2 }\ and\ -\sqrt 2

Q1 (iv) Find the roots of the following quadratic equations by factorization: 2x^2 -x + \frac{1}{8} = 0

Answer:

Given the quadratic equation: 2x^2 -x + \frac{1}{8} = 0

Solving the quadratic equations, we get

16x^2-8x+1 = 0

Factorization gives, \Rightarrow 16x^2-4x-4x+1 = 0

\Rightarrow 4x(4x-1)-1(4x-1) = 0

\Rightarrow (4x-1)(4x-1) = 0

\Rightarrow x=\frac{1}{4}\ or\ \frac{1}{4}

Hence, the roots of the given quadratic equation are

\frac{1}{4}\ and\ \frac{1}{4}

Q1 (v) Find the roots of the following quadratic equations by factorization: 100x^2 -20x +1 = 0

Answer:

Given the quadratic equation: 100x^2 -20x +1 = 0

Factorization gives, 100x^2 -10x-10x +1 = 0

\Rightarrow 10x(10x-1)-10(10x-1) = 0

\Rightarrow (10x-1)(10x-1) = 0

\Rightarrow x=\frac{1}{10}\ or\ \frac{1}{10}

Hence, the roots of the given quadratic equation are

\frac{1}{10}\ and\ \frac{1}{10} .

Q2 Solve the problems given in Example 1. (i) x^2-45x+324 = 0 (ii) x^2-55x+750 = 0

Answer:

From Example 1 we get:

Equations:

(i) x^2-45x+324 = 0

Solving by factorization method:

Given the quadratic equation: x^2-45x+324 = 0

Factorization gives, x^2-36x-9x+324 = 0

\Rightarrow x(x-36) - 9(x-36) = 0

\Rightarrow (x-9)(x-36) = 0

\Rightarrow x=9\ or\ 36

Hence, the roots of the given quadratic equation are x=9\ and \ 36 .

Therefore, John and Jivanti have 36 and 9 marbles respectively in the beginning.

(ii) x^2-55x+750 = 0

Solving by factorization method:

Given the quadratic equation: x^2-55x+750 = 0

Factorization gives, x^2-30x-25x+750 = 0

\Rightarrow x(x-30) -25(x-30) = 0

\Rightarrow (x-25)(x-30) = 0

\Rightarrow x=25\ or\ 30

Hence, the roots of the given quadratic equation are x=25\ and \ 30 .

Therefore, the number of toys on that day was 30\ or\ 25.

Q3 Find two numbers whose sum is 27 and the product is 182.

Answer:

Let two numbers be x and y .

Then, their sum will be equal to 27 and the product equals 182.

x+y = 27 ...............................(1)

xy =182 .................................(2)

From equation (2) we have:

y = \frac{182}{x}

Then putting the value of y in equation (1), we get

x+\frac{182}{x} = 27

Solving this equation:

\Rightarrow x^2-27x+182 = 0

\Rightarrow x^2-13x-14x+182 = 0

\Rightarrow x(x-13)-14(x-13) = 0

\Rightarrow (x-14)(x-13) = 0

\Rightarrow x = 13\ or\ 14

Hence, the two required numbers are 13\ and \ 14 .

Q4 Find two consecutive positive integers, the sum of whose squares is 365.

Answer:

Let the two consecutive integers be 'x'\ and\ 'x+1'.

Then the sum of the squares is 365.

. x^2+ (x+1)^2 = 365

\Rightarrow x^2+x^2+1+2x = 365

\Rightarrow x^2+x-182 = 0

\Rightarrow x^2 - 13x+14x+182 = 0

\Rightarrow x(x-13)+14(x-13) = 0

\Rightarrow (x-13)(x-14) = 0

\Rightarrow x =13\ or\ 14

Hence, the two consecutive integers are 13\ and\ 14 .

Q5 The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

Answer:

Let the length of the base of the triangle be b\ cm .

Then, the altitude length will be: b-7\ cm .

Given if hypotenuse is 13\ cm .

Applying the Pythagoras theorem; we get

Hypotenuse^2 = Perpendicular^2 + Base^2

So, (13)^2 = (b-7)^2 +b^2

\Rightarrow 169 = 2b^2+49-14b

\Rightarrow 2b^2-14b-120 = 0 Or b^2-7b-60 = 0

\Rightarrow b^2-12b+5b-60 = 0

\Rightarrow b(b-12) + 5(b-12) = 0

\Rightarrow (b-12)(b+5) = 0

\Rightarrow b= 12\ or\ -5

But, the length of the base cannot be negative.

Hence the base length will be 12\ cm .

Therefore, we have

Altitude length = 12cm -7cm = 5cm and Base length = 12\ cm

Q6 A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.

Answer:

Let the number of articles produced in a day = x

The cost of production of each article will be =2x+3

Given the total production on that day was Rs.90 .

Hence we have the equation;

x(2x+3) = 90

2x^2+3x-90 = 0

\Rightarrow 2x^2+15x-12x-90 = 0

\Rightarrow x(2x+15) - 6(2x+15) = 0

\Rightarrow (2x+15)(x-6) = 0

\Rightarrow x =-\frac{15}{2}\ or\ 6

But, x cannot be negative as it is the number of articles.

Therefore, x=6 and the cost of each article = 2x+3 = 2(6)+3 = 15

Hence, the number of articles is 6 and the cost of each article is Rs.15.

More About NCERT Solutions for Class 10 Maths Exercise 4.2: Quadratic Equations

Exercise 4.2 Class 10 Maths consists of a question based on the solution of a quadratic equation by factorisation. The most important method in factorization is splitting of the middle term. In order to solve the quadratic equations by Factorisation, we need to arrange the terms in the form of ax2+bx+c=0 . Then we need to find the product of the first and last terms of the given expression. Next, we need to try to split the middle term into two terms but their product should be equal to the product of the first and last terms of the expression. Finally, we need to group the terms to factorize the given expression. The NCERT solutions for Class 10 Maths exercise 4.2 basically centred on the concepts of understanding quadratic conditions. Scientifically, the roots of the condition and the zeroes of the polynomial are the same. There must be at least two roots/zeros for a quadratic condition as given in exercise 4.2 Class 10 Maths. Also students can get access of Quadratic Equations Class 10 Notes to revise all the concepts quickly.

Benefits of NCERT Solutions for Class 10 Maths Exercise 4.2:

  • NCERT solutions for Class 10 Maths exercise 4.2 helps in solving the problems in a step-by-step manner which is essential to avoid confusion for you.
  • If you go through the NCERT solution for Class 10th Maths chapter 4 exercise 4.2, we can gain more knowledge about quadratic equations. Since it is an important exercise, you need to practice all the questions at least twice.
  • Exercise 4.2 Class 10 Maths, is based on tackling the arrangements of the quadratic equations by factorisation and their roots which are imperative concepts of the chapter.

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As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters

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NCERT Solutions of Class 10 Subject Wise

Subject Wise NCERT Exemplar Solutions

Frequently Asked Questions (FAQs)

1. What is the general form of the quadratic equation?

The common shape of the quadratic condition is ax62+bx+c=0 where a, b, c are real numbers. 

2. Whether the roots of the condition and the zeroes of the condition are the same ?

Yes, the roots of the equation and the zeroes of the equation are the same. 

3. Factorize the polynomial a^2-10a+24 .

a^2-10a+24=a2-4a-6a+24 

=a(a-4)-6(a-4) 

=(a-4)(a-6)  

4. What is the vital condition for understanding the quadratic conditions by utilizing the strategy of factorization?

In the strategy of factorization, the product of 1st and final terms of a given condition must be broken even with the product of 2nd and 3rd terms of the same given condition. 

5. What is the splitting of the middle term?

Splitting of the middle term is nothing but we have to rewrite the middle term of the quadratic expression as the sum or difference of the two terms, that is we have to split the middle term into two parts in terms of sum or difference of the terms. 

6. What is the sum product form according to NCERT solutions for Class 10 Maths chapter 4 exercise 4.2 ?

The sum-product form is nothing but in the equation ax^2+bx+c=0 , the product of the middle term after splitting must be equal to a×c and the sum must be equal to b.

7. How numerous questions and what sort of questions are secured inside the NCERT solutions for Class 10 Maths chapter 4 exercise 4.2 ?

NCERT solutions for Class 10 Maths chapter 4 exercise 4.2 comprises of six questions which are based on the factorization strategy.

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