NCERT Solutions For Class 10 Maths Chapter 4: Quadratic Equations

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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.
An umbrella has 8 ribs which are equally spaced (see Fig. 11.10). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.

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2.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:\(\frac{(\text{1 + tan² A})}{(\text{1 + cot² A})} = (\frac{\text{1 - tan A }}{\text{ 1 - cot A}})^²= \text{tan² A}\)

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3.
Solve the following pair of linear equations by the substitution method.
(i) x + y = 14
x – y = 4
(ii) s – t = 3
  \(\frac{s}{3} + \frac{t}{2}\) =6
(iii) 3x – y = 3
9x – 3y = 9
(iv) 0.2x + 0.3y = 1.3
0.4x + 0.5y = 2.3
(v)\(\sqrt2x\) + \(\sqrt3y\)=0
  \(\sqrt3x\) - \(\sqrt8y\) = 0
(vi) \(\frac{3x}{2} - \frac{5y}{3}\) =-2,
  \(\frac{ x}{3} + \frac{y}{2}\) = \(\frac{ 13}{6}\)

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4.
Form the pair of linear equations for the following problems and find their solution by substitution method.
(i) The difference between two numbers is 26 and one number is three times the other. Find them.
(ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
(iii) The coach of a cricket team buys 7 bats and 6 balls for Rs 3800. Later, she buys 3 bats and 5 balls for Rs 1750. Find the cost of each bat and each ball.
(iv) The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs 105 and for a journey of 15 km, the charge paid is Rs 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km.
(v) A fraction becomes\(\frac{ 9}{11}\), if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes \(\frac{5}{6}\). Find the fraction.
(vi) Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?

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5.
A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.

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6.
The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table :
Length (in mm)
Number of leaves
118 - 126
3
127 - 135
5
136 - 144
9
145 - 153
12
154 - 162
5
163 - 171
4
172 - 180
2
Find the median length of the leaves.
(Hint : The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to 117.5 - 126.5, 126.5 - 135.5, . . ., 171.5 - 180.5.)

Length (in mm)	Number of leaves
118 - 126	3
127 - 135	5
136 - 144	9
145 - 153	12
154 - 162	5
163 - 171	4
172 - 180	2

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NCERT Solutions For Class 10 Maths Chapter 4: Quadratic Equations

NCERT Solutions for Class 10 Mathematics Chapter 4

Important Topics in Class 10 Maths Chapter 4

NCERT Solutions For Class 10 Maths Chapter 4 Exercises:

CBSE X Related Questions

1.
An umbrella has 8 ribs which are equally spaced (see Fig. 11.10). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.

2.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:\(\frac{(\text{1 + tan² A})}{(\text{1 + cot² A})} = (\frac{\text{1 - tan A }}{\text{ 1 - cot A}})^²= \text{tan² A}\)

Similar Mathematics Concepts

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NCERT Solutions For Class 10 Maths Chapter 4: Quadratic Equations

NCERT Solutions for Class 10 Mathematics Chapter 4

Important Topics in Class 10 Maths Chapter 4

NCERT Solutions For Class 10 Maths Chapter 4 Exercises:

CBSE X Related Questions

1. An umbrella has 8 ribs which are equally spaced (see Fig. 11.10). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.

2. Prove the following identities, where the angles involved are acute angles for which the expressions are defined:\(\frac{(\text{1 + tan² A})}{(\text{1 + cot² A})} = (\frac{\text{1 - tan A }}{\text{ 1 - cot A}})^²= \text{tan² A}\)

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
An umbrella has 8 ribs which are equally spaced (see Fig. 11.10). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.

2.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:\(\frac{(\text{1 + tan² A})}{(\text{1 + cot² A})} = (\frac{\text{1 - tan A }}{\text{ 1 - cot A}})^²= \text{tan² A}\)