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

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

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1. What is a quadratic equation?

Answer: Any equation that can be rearranged into the following standard form:

ax² + bx + c = 0, is called a quadratic equation. In a quadratic equation, x is an unknown variable and there have to one or more squared terms of x. The coefficients of x, that is a, b and c are constant terms. Also, a cannot have the value of zero, since it will make cancel out the square term of x, changing it into a linear equation.

There are always two solutions to a quadratic equation, one positive term whereas the other is a negative term.

2. What is the nature of the roots of a quadratic equation?

Answer: The number of roots of an equation depends on its degree, that is, the number of roots of an equation is equal to the degree of the equation. Therefore, a quadratic equation has two roots, a positive root, and the other a negative root. The nature of the roots of a quadratic equation can be real, imaginary, and zero.

The nature of the roots of a quadratic equation depends on its discriminant, that is, equal to D = b² - 4ac.

Now, if D < 0, that is, if b² - 4ac < 0, then the roots of the quadratic equation are unequal and imaginary.

If D = 0, that is, if b² - 4ac = 0, then the roots of the quadratic equation are equal and real.

If D > 0, that is, if b² - 4ac > 0, and also, D is a perfect square, then the roots of the quadratic equation are unequal, real, and rational. If D > 0, that is, if b² - 4ac > 0, and D is not a perfect square, then the roots are unequal, real, and irrational.

3. How to solve quadratic equation sums of class 10 Chapter 4 NCERT Maths?

Answer: In Chapter 4 of Class 10 NCERT Maths, the various concepts related to quadratic equations are explained with examples. It is necessary for students to understand how to identify a quadratic equation, as the very first thing. Rearranging the equations into the standard form of a quadratic equation is the first step in solving a quadratic equation. This will become easy, with the first few sums of the exercise 4.1 of Class 10 NCERT Maths Chapter 4.

The most important step to solve a quadratic equation is to factorize the middle term of the equation. After the factorization is completed, the roots of the quadratic equation can be found out.

4. Why should you refer to the NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations (Ex. 4.1) Exercise 4.1?

Answer: The chapter on quadratic equations is one of the most important chapters for class 10 maths board examinations. So a sound understanding of all the concepts in this chapter as well all types of problems is imperative. The NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations (Ex. 4.1) Exercise 4.1 available on Vedantu are prepared by our subject matter experts. All the sums are solved in a step by step manner, explaining the logic behind it. Thereby making it easier to understand for all students.