NCERT Solutions for Class 10 Maths Chapter 4- Quadratic Equations Exercise 4.4

The course syllabus for Class 10 can be demanding, but with a little preparation, students can feel confident tackling the material. Solving practise problems using the NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.4 offered by Extramarks is one of the finest strategies for students to be ready for the Class 10 Mathematics board exam. For instance, in Mathematics, practising several different question types may help students feel more at ease with the course subject. In the end, it is critical to be organised throughout the Class 10 academic year. Students who remain on top of their studies might benefit from keeping track of their assignments, examinations, and quizzes.

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NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations (Ex 4.4) Exercise 4.4

The full form of NCERT stands for National Council of Educational Research and Training, which was founded in 1961 and offers students a number of services and advantages. The Ministry of Education, a division of the Indian Government, established the NCERT as an educational organisation and independent intelligence service.

There are books called NCERT Solutions that have all the questions and solutions from the NCERT textbooks for classes 6 to 12. Extramarks’ NCERT Solutions on their website emphasise the importance of students in Classes 6 to 12 using NCERT SolutionsStudents can explore the NCERT Solutions for corresponding classes on Extramarks’ website in the format of NCERT Solutions Class 12, NCERT Solutions Class 11, NCERT Solutions Class 10, NCERT Solutions Class 9, NCERT Solutions Class 8, NCERT Solutions Class 7, and NCERT Solutions Class 6. These solutions can be very effective and convenient for students who want to prepare for their examinations.

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There are a few relevant topics that are covered in Class 10 Maths Chapter 4 Exercise 4.4 which are given below:

  • Nature of roots of the Quadratic Equations
  • The value of Discriminant

By practising the NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.4, students can solve the questions related to the Nature of roots quickly. Extramarks’ website helps students to download the NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.4 and other solutions in PDF format when the examinations areapproaching.

Students must download the NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.4 in PDF layout from the Extramarks website to acquire detailed information about how to solve the Quadratic Equations with the help of different formulas. The NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.4 can be downloaded from the Extramarks mobile application or website.

Access NCERT Solutions for Class-10 Maths Chapter 4 – Quadratic Equations

The NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.4 provides in-depth solutions that are supplied for each question to students. Extramarks’ NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.4 includes a substantial number of unanswered questions, practise tests, and past years’ papers that support students in adequately preparing for their exams.

Students may enhance their problem-solving abilities by utilising the services provided on  Extramarks’ mobile app and website. Extramarks’ facilities are very useful for providing students with Revision Notes or NCERT Solutions.NCERT Solutions for Class 10 Maths, Chapter 4, Exercise 4.4, on the other hand, assists students in effectively understanding mathematics.It is essential for students to use the NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.4 while they study and prepare for their examinations. Students will benefit from the fact that the NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.4 give them factual knowledge of the subjects covered in the Mathematics NCERT textbook.

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Class 10 Maths Chapter 4

Chapter 4 of the subject Mathematics in Class 10 is Quadratic Equations. Quadratic Equations are the Mathematical equations that consist of any formula that may be transformed into standard form, including ax2 + bx + c = 0.

Equations in Mathematics that have a squared variable are known as Quadratic Equations. The three different types of Quadratic Equations are Cubic, Quadratic, and Linear. The Quadratic Formula is used to solve the Quadratic Equation, which is the most challenging of the three.

The Mathematical equation known as the Quadratic Formula is used to resolve Quadratic Equations.

The Quadratic Formula is:

x = −b ± √b2 − 4ac2

Where:

x is the solution to the equation

b is the coefficient of the squared variable

a is the coefficient of the variable

c is the constant

Quadratic Equations have a variety of real-world applications. One such application is in the field of Engineering. Engineers often use Quadratic equations to model the motion of objects. For example, they might use a Quadratic equation to model the motion of a car as it speeds up and slows down. Quadratic equations can also be used to duplicate the motion of objects in planetary orbits.

Another real-world application of Quadratic equations is in the field of Economics. Economists often use Quadratic equations to model the behaviour of financial markets. For example, they might use a Quadratic equation to replicate the behaviour of stock prices.

Contrary to that, Quadratic equations can be used in the Physical Sciences. Physicists frequently use Quadratic equations to copy the actions of gases. For example, they may use a Quadratic equation to model the behaviour of air pressure.

Importance of NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.4

NCERT Solutions are collections of questions and solutions that may be found on the Extramarks website. These NCERT Solutions are made to aid students in their examinations and provide them with a deeper comprehension of the subjects covered in the syllabus.The NCERT Solutions are helpful to many students since they not only help them understand the topics better but also provide answers to their queries.

The use of NCERT Solutions has several advantages. Students can search for the matching solutions on Extramarks’ website if they are having trouble understanding a concept in the textbook. This might aid in their academic improvement and help them understandthe subject better.

Taking advantage of NCERT Solutions also helps students study for tests, which is an additional benefit. Each problem is thoroughly addressed in the solutions, which suggest a detailed description of how to solve it. Last but not least, using NCERT Solutions can assist in analytical development.

The NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.4 can be helpful in order to better understand the subject content. Moreover, because the NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.4 are straightforward to memorise and follow, students can successfully study for their exams with their assistance.Further, the solutions could help students enhance their Mathematical aptitudes. Extramarks’ NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.4 should be fully utilised by students looking for answers to NCERT Textbook questions.Solved Examples

The NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.4 provides students with examples and solutions to intext problems. Students can find out the Chapters, theorems, and formulas to be used in solving the queries by using NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.4 which involves solved questions with clear solutions. These NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.4 can be used to get solutions efficiently.

NCERT Solutions for Class 10 Maths Chapter 4 Exercises

There are in total 4 Exercises in Chapter 4, Quadratic Equations of Class 10. Each exercise holds different concepts and importance. In Exercise 4.1 students can discover questions related to the Quadratic Equation, how to solve them if certain scenarios occur, and the present age of a person. Exercise 4.2 is all about solving Quadratic Equations and obtaining their roots with the help of Factorisation.

On the other hand, in Exercise 4.3 students can explore the questions regarding solving the Quadratic Equations by Completing the square and Quadratic formula. Finally, Class 10 Maths Ch 4 Ex 4.4 of Quadratic Equations focuses on how to solve these equations using the Nature of Roots and determining the discriminants of the equations.. If students want to solve the questions mentioned in Class 10 Chapter 4 Exercise 4.4, they can check the NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.4 on the Extramarks website. These solutions are approved by the experts and, hence, are exact and trustworthy.

NCERT Solutions for Class 10 Maths PDFs (Chapter-wise)

The NCERT Solutions, for example, NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.4 guides students in solving queries without making any Mathematical errors or mistakes. The solutions suggested by Extramarks are reviewed by subject matter experts or specialists. This advantage helps students to rely on them without any confusion. The Chapters that are there in the Mathematics NCERT Textbook of Class 10 are as follows:

  1. Real Numbers
  2. Polynomials
  3. Pair of Linear Equations in Two Variables
  4. Quadratic Equations
  5. Arithmetic Progressions
  6. Triangles
  7. Coordinate Geometry
  8. Introduction to Trigonometry
  9. Some applications of Trigonometry
  10. Circles
  11. Constructions
  12. Areas Related to Circles
  13. Surface Areas and Volumes
  14. Statistics
  15. Probability

 

The solutions for the chapters introduced in the Mathematics textbook of Class 10 can be found on the website of Extramarks. For the solutions for Class 10 Mathematical questions, students can download the mobile application of Extramarks and take benefit of its facilities.

 

Extramarks is a resource that students should use if they need NCERT Solutions for Class 10 Maths, Chapter 4, Exercise 4.4, and to help them with their queries.The solutions presented in NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.4 are precise and correct since they were created by specialised professionals. Students cannot find any flaws in the solutions that Extramarks is referring to. The NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.4, available on the Extramarks website, allow students to obtain reliable and detailed solutions.

Q.1

Find the nature of the roots of the following quadraticequations. If the real roots exist, find them.(i) 2x2−3x+5=0 (ii)  3x2−43x+4=0(iii) 2x2−6x+3=0

Ans.

(i) 2x2−3x+5=0 Here, a=2, b=−3, c=5 Therefore, discriminant b2−4ac=−32−4×2×5                                                                          = 9−40                                                                          =−31<0 So, the given equation has no real roots.(ii)  3x2−43x+4=0 Here, a=3, b=−43, c=4 Therefore, discriminant b2−4ac=−432−4×3×4                                                                          = 48−48                                                                          =0 So, the given equation has two equal real roots. The roots are −b2a,  −b2a,   i.e., 436,  436, i.e., 23, 23.(iii) 2x2−6x+3=0 Here, a=2, b=−6, c=3 Therefore, discriminant b2−4ac=−62−4×2×3                                                                             =36−24                                                                             =12>0 So, the given equation has two distinct real roots. The roots are given by −b+b2−4ac2a and  −b–b2−4ac2a. −b±b2−4ac2a=6±124=3±32 Hence, the roots are 3+32 and 3−32.

Q.2 Find the values of k for each of the following quadratic equations, so that they have two equal roots.
(i) 2x2 + kx +3 = 0
(ii) kx(x – 2) + 6 = 0

Ans.

(i) 2x2+kx+3=0 Discriminant must be zero for two roots of the given equation to be equal. Therefore, b2−4ac=0⇒ k2−4×2×3=0⇒k2−24=0⇒k2=24⇒k=24=±26(ii)         kx(x−2)+6=0⇒kx2−2kx+6=0 Discriminant must be zero for two roots of the given equation to be equal. Therefore, b2−4ac=0⇒ 4k2−4×k×6=0⇒k2−6k=0⇒k(k−6)=0⇒k=0 or k=6But k=0 does not satisfy the given equation.Thus, the given equation has equal roots if the value of k is 6 only.

Q.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.

Ans.

Let breadth of the rectangular mango grove is x.According to question,       x×2x=800⇒x2=400⇒x2−400=0Discriminant=b2−4ac=0−4×1×(−400)=1600>0Therefore, the above equation has two distinct real roots.Now,      x2−400=0⇒x2=400⇒x=±20But breadth can not be negative.So, x=20 and 2x=40Hence, length=40 m                breadth=20 m

Q.4 Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

Ans.

Let age of one friend be x years.Age of the other friend =(20−x) yearsAccording to question,       (x−4)(20−x−4)=48⇒(x−4)(16−x)=48⇒−x2+16x−64+4x−48=0⇒x2−20x+112=0Discriminant=b2−4ac=(−20)2−4×112=400−448=−48<0Therefore, no real root is possible and so the given situationis not possible.

Q.5 Is it possible to design a rectangular park of perimeter 80 m and area 400 m2? If so, find its length and breadth.

Ans.

Let length and breadth of the rectangular park be x.and y respectively.According to question, we have       2(x+y)=80⇒x+y=40⇒y=40−x                                            ...(1)Also, we have      xy=400⇒x(40−x)=400⇒40x−x2=400⇒x2−40x+400=0Discriminant=b2−4ac=(−40)2−4×400=0So, the above equation has two equal real roots.Now, x2−40x+400=0⇒(x−20)2=0⇒x=20 or x=20From equation (1), we have          y=40−x=40−20=20Hence, length and breadth of the rectangular park are20 m and 20 m respectively.

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FAQs (Frequently Asked Questions)

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