## NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations (Ex 4.1) Exercise 4.1

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## FAQs on NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations (Ex 4.1) Exercise 4.1

**1.The Altitude of a Right Triangle is 7 cm Less than its Base. If the Hypotenuse is 13 cm, Find the Other Two Sides.**

You can find the following in class 10 Maths ex 4.1 solutions:

Let x be the base, the altitude will be x - 7

Now as per Pythagoras theorem,

x^{2} + (x − 7)2 = 13^{2}

= x^{2} + x^{2} - 14x + 49 = 169

= 2x^{2} -14x = 120

= x^{2} - 7x = 60

= x^{2} - 12x + 5x - 60 = 0

= x(x - 12) + 5(x - 12) = 0

= (x - 12) (x + 5) = 0

x = 12 or -5

Since x cannot be negative x = 12.

So base is 12 cm and altitude is (12 - 7) = 5 cm.

**2. If Zeba were Younger by 5 years than what she really is then the Square of her age Would have been 11 more than five times her actual age. What is her age now?**

The solution according to exercise 4.1 class 10 Maths NCERT solutions is as follows:

Let age of Zeba be x years

As per the question:

(x − 5)^{2} = 11 + 5x(x − 5)^{2} = 11 + 5x

=> x^{2} + 25 − 10x = 11 + 5x(x)^{2} + 25 − 10x = 11 + 5x

=> x^{2} − 15x + 14 = 0 x 2 − 15x + 14 = 0 x 2 − 14x − x + 14 = 0 x 2 − 14x − x + 14 = 0

=> (x - 1)(x - 14)

Therefore, age of Zeba is 14 years.

**3. What is a Quadratic Equation, and what is its general form?**

When a quadratic order polynomial is of the type ax^{2} + bx + c = 0 (a ≠ 0), we call it a Quadratic Equation. The general version of the Quadratic Equation is now ax^{2} + bx + c = 0 (a ≠ 0), where ‘a', ‘b' and ‘c’ are constants i.e. numbers. The constant ‘b’ and ‘c’ can also be equal to zero but ‘a’ cannot be zero.

**4. How many questions are there in Chapter 4 Maths Class 10?**

There are a total of four exercises. In the first exercise, there are two questions. In the second, there are six; in the third, there are 11; and in the fourth exercise, there are five. So, all in all, there are 23 questions and some of these questions have some sub-parts too. In the, NCERT Solutions for Class 4, Maths Chapter 4 there are solved examples as well that will help in preparation for the board exams.

**5. How to find the nature of roots?**

The term b^{2} – 4ac is called the discriminant of a quadratic equation since b^{2} – 4ac determines whether the quadratic equation ax^{2} + bx + c = 0 has real roots or not. So, a Quadratic Equation ax^{2}^{ }+ bx + c = 0 has

(i) two distinct real roots, if b^{2} – 4ac > 0,

(ii) two equal real roots, if b^{2} – 4ac = 0,

(iii) no real roots, if b^{2} – 4ac < 0.

**6. How can I top in Class 10 Maths?**

In order to score the best marks in Maths, regular practice is required. You must practice and revise all the solved examples and questions given in the NCERT book. You must all be thorough with all the concepts, theorems and formulae of all the chapters. You can visit the page NCERT Solutions for Class 10 Maths, on the official website of Vedantu for a complete guide.

**7. Where can I get the NCERT Solution for Class 10 Chapter 4 Maths?**

You can easily access the NCERT Solutions for Class 10 Maths, on the Vedantu official website (vedantu.com) and on the Vedantu app absolutely free of cost. You can also get revision notes and other study material free of cost on the Vedantu website (vedantu.com). The answers are provided comprehensively and are very easy to understand; all the formulae used in the questions are also provided along with the answers to facilitate a quick revision.