NCERT Solutions for Class 10 Maths Chapter 4 Ex 4.3 are created by askIITians Maths experts to help you master this exercise. Chapter 4 Quadratic Equations is an important chapter from the board exams point of view as well as for competitive exams like JEE and NEET. Exercise 4.3 is based on finding the solution of a quadratic equation by the method of completing the square. Our NCERT Solutions are going to help you form a complete understanding of this exercise so that you can solve any type of question-based on it. You can download our NCERT Solutions in PDF form and study them at your convenience and pace.
The third exercise of Chapter 4 Quadratic Equations is based on finding the solution of a quadratic equation based on the method of completing the square. In this method, you have to convert the quadratic equation to square form and find its solution. You are also introduced to the quadratic formula in this exercise. Given below are some important points related to Class 10 Maths Chapter 4 4 Quadratic Equations Ex 4.3:
Quadratic Equations: A quadratic equation in the variable x is of the form ax2 + bx + c = 0, where a, b, c are real numbers and a ≠ 0.
Quadratic Formula: The roots of a quadratic equation are given by using the quadratic formula:
where a, b and c are the real numbers and b2 – 4ac is called the discriminant.
Nature of Roots: A quadratic equation ax2 + bx + c = 0 has
(i) two distinct real roots, if b2 – 4ac > 0,
(ii) two equal roots (i.e., coincident roots), if b2 – 4ac = 0, and
(iii) no real roots, if b2 – 4ac < 0.
Types of questions included in NCERT Class 10 Maths Chapter 4 Ex 4.3:
Ex 4.3 Q1: In this question, you are given some quadratic equations and you have to find their roots using the method of completing the squares.
Ex 4.3 Q2: In this question, you have to find the roots of the quadratic equations given in Q1 using the quadratic formula. Both these questions are straightforward.
Ex 4.3 Q3: In this question, you are given two quadratic equations and you have to find their roots. You may choose any method to find the roots.
Ex 4.3 Q4: This question is based on finding ages. These types of questions are often included in olympiads and competitive exams. In this question, you are given that the sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is 1/3. You have to find his present age.
Ex 4.3 Q5: In this question, you are given that the sum of Shefali’s marks in Mathematics and English is 30. If she had got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. You have to find her marks in the two subjects.
Ex 4.3 Q6: In this question, you are given that the diagonal of a rectangular field is 60 meters more than the shorter side. If the longer side of the field is 30 meters more than the shorter side, you have to find sides of the field. You can see that in word problems like these you not only have to find the solutions of quadratic equations, but you also have to formulate these equations by yourself.
Ex 4.3 Q7: In this question, you are given that the difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. You have to find the two numbers. Check our NCERT Solutions for Class 10 Maths Chapter 4 Ex 4.3 to understand how to solve this question stepwise.
Ex 4.3 Q8: In this question, you have to find the speed of a train, given that the train travels 360 km at a uniform speed. Also, if the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. These types of questions are important from the exam point of view.
Ex 4.3 Q9: This question is based on water pipes. You are given that there are two water taps. The tap of a larger diameter takes 10 hours less than the smaller one to fill the tank separately. Together, these taps can fill the tank in 9X3/8 hours.
Ex 4.3 Q10: In this question, you are given that an express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11km/h more than that of the passenger train, you have to find the average speed of the two trains.
Ex 4.4 Q11: In the last question of this exercise, you are given that the sum of the areas of two squares is 468 m2. If the difference of their perimeters is 24 m, you have to find the sides of the two squares.
Students face different challenges while solving Ex 4.3 of the Quadratic Equations chapter. This is because you not only have to solve the equation but also have to form correct quadratic equations in most of the questions. Any single mistake here can lead you to a completely different final answer. Sometimes students make silly mistakes by interchanging the + sign with the - sign and vice-versa. This also leads them to wrong answers. This is why we have created stepwise NCERT Solutions for Class 10 students so that they can rectify their mistakes at an early stage and prepare well for the board exams.
Key benefits of NCERT Solutions for Class 10 Maths Exercise 4.3:
The third exercise of Chapter 4 Quadratic Equations includes 11 questions. There are word problems and short answer questions included in this exercise.
The NCERT Solutions are prepared by our expert Maths faculty members who have more than 15 years of online teaching experience. The solutions include comprehensive explanations and are based on the latest exam pattern. We guarantee that our NCERT Class 10 Maths solutions will help in solidifying all your concepts.
The Quadratic Equations chapter of Class 10 Maths is based on how to find the solution to a quadratic equation using factoring and completing the square methods. It also includes how to identify the nature of the roots of a quadratic equation.