NCERT Solutions For Class 10 Maths Chapter 4: Quadratic Equations

Education Journalist | Study Abroad Strategy Lead

The NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations are given in this article. Quadratic Equations are polynomial equations with the degree of the equation equal to 2 in one variable shape. For example: f(x) = ax² + bx + c in which a, b, c, ∈ r and a ≠ 0. The values that fulfil a given quadratic equation are called roots and each equation has at least 2 roots.

Class 10 Maths Chapter 4 Quadratic Equations belongs to Unit 2 Algebra which has a weightage of 20 marks in the CBSE Class 10 Maths Examination. Questions related to finding the nature of roots of Quadratic Equation and Quadratic Equations Formula are often asked in the examination.

Download PDF: NCERT Solutions for Class Class 10 Mathematics Chapter 4

NCERT Solutions for Class 10 Mathematics Chapter 4

NCERT Solutions

Important Topics in Class 10 Maths Chapter 4

A polynomial of the form ax²+ bx + c, where a, b and c are real numbers and a is not equal to 0 is known as a quadratic polynomial.

Any equation of the form p(x) = c, where p(x) is any polynomial of degree 2 and c is a constant, can be identified as a quadratic equation.

The roots of quadratic equation are the values of x for which a quadratic equation is satisfied.

A quadratic equation can either have 2 distinct real roots, 2 equal roots or the real roots for the equation may not exist.

Quadratic Formula can be used to directly find the roots of a quadratic equation from its standard form.

For the quadratic equation ax²+ bx + c = 0, x = [-b ± √(b²-4ac)]/2a

Discriminant of the Quadratic Equation – For a quadratic equation ax²+ bx + c = 0, the expression b²− 4ac is known as the discriminant, (denoted by D).

The discriminant determines the nature of the roots of the quadratic equation based on its coefficients.

Based on the discriminant value, D = b²− 4ac, the quadratic equation roots can be of three types.

Case 1: If D > 0, the equation has two distinct real roots.

Case 2: If D = 0, the equation has two equal real roots.

Case 3: If D < 0, the equation has no real roots.

NCERT Solutions For Class 10 Maths Chapter 4 Exercises:

The detailed solutions for all the NCERT Solutions for Quadratic Equations under different exercises are as follows:

Quadratic Equations – Related Topics:

Nature of Roots	Discriminant Formula	Quadratic Interpolation Formula
Quadratic Equations Formula	Quadratic Equations MCQ	Degree of Polynomial
Polynomials Formula	Factorisation of Polynomials	Roots of Polynomials

CBSE Class 10 Maths Study Guides:

NCERT Solutions for Class 10 Maths	Math Formula	Class 10 Maths Notes
Geometry	Maths Study Material	Mensuration
Difference between in Maths	Calculus	Math MCQs

CBSE X Related Questions

1.
Which of the following sequence is \(\textit{not }\)an A.P. ?
- \( 2, \frac{5}{2}, 3, \frac{7}{2}, \dots \)
- \( -1.2, -3.2, -5.2, -7.2, \dots \)
- \( \sqrt{2}, \sqrt{8}, \sqrt{18}, \dots \)
- \( 1^2, 3^2, 5^2, 7^2, \dots \)
View Solution
2.
The graph of \(y = f(x)\) is given. The number of zeroes of \(f(x)\) is :
- 0
- 1
- 3
- 2
View Solution
3.
Aarush bought 2 pencils and 3 chocolates for Rs 11 and Tanish bought 1 pencil and 2 chocolates for Rs 7 from the same shop. Represent this situation in the form of a pair of linear equations. Find the price of 1 pencil and 1 chocolate, graphically.
View Solution
4.
Three tennis balls are just packed in a cylindrical jar. If radius of each ball is \(r\), volume of air inside the jar is
- \(2\pi r^3\)
- \(3\pi r^3\)
- \(5\pi r^3\)
- \(4\pi r^3\)
View Solution
5.
In the given figure, \( \triangle AHK \sim \triangle ABC \). If \( AK = 10 \text{ cm} \), \( BC = 3.5 \text{ cm} \) and \( HK = 7 \text{ cm} \), find the length of \( AC \).
View Solution
6.
Assertion (A) : H.C.F. \((36 m^{2}, 18 m) = 18 m\), where \(m\) is a prime number.
Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.
- Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- Assertion (A) is true, but Reason (R) is false.
- Assertion (A) is false, but Reason (R) is true.
View Solution