NCERT Solutions For Class 10 Maths Chapter 4 Quadratic Equations Ex 4.1


NCERT Solutions For Class 10 Maths Chapter 4 Quadratic Equations Ex 4.1

NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.1 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.1.

BoardCBSE
TextbookNCERT
ClassClass 10
SubjectMaths
ChapterChapter 4
Chapter NameQuadratic Equations
ExerciseEx 4.1
Number of Questions Solved2
CategoryNcertcareer

Ex 4.1 Class 10 Maths Question 1.
Check whether the following are quadratic equations:
(i) (x+ 1)2=2(x-3)
(ii) x – 2x = (- 2) (3-x)
(iii) (x – 2) (x + 1) = (x – 1) (x + 3)
(iv) (x – 3) (2x + 1) = x (x + 5)
(v) (2x – 1) (x – 3) = (x + 5) (x – 1)
(vi) x2 + 3x + 1 = (x – 2)2
(vii) (x + 2)3 = 2x(x2 – 1)
(viii) x3 -4x2 -x + 1 = (x-2)3
Solution:
NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.1 Free PDF Download Q1
NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.1 PDF Download Q1.1
NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.1 PDF Q1.2

NCERT Solutions Class 10 Maths chapter 4 Quadratic Equations- Video

You can also watch the video solutions of NCERT Class10 Maths chapter 4 Quadratic Equations here.

https://youtube.com/watch?v=videoseries%3Flist%3DPLXX3lyEZ5Op5LdAkjdB8hW9qcL0Hh26SB

Ex 4.1 Class 10 Maths Question 2.
Represent the following situations in the form of quadratic equations:
(i) The area of a rectangular plot is 528 m2. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.
(ii) The product of two consecutive positive integers is 306. We need to find the integers.
(iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.
(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.
Solution:
Quadratic Equations Class 10 Maths NCERT Solutions Chapter 4 Ex 4.1 Q2
Chapter 4 Maths Class 10 NCERT Solutions Ex 4.1 Q2.1

NCVT Mis Result 2019

NCERT Solutions Class 10 Maths chapter 4 Quadratic Equations

Class 10, Maths chapter 4, Quadratic Equations solutions are given below in PDF format. You can view them online or download PDF file for future use.

or save the solution images and take the print out to keep it handy for your exam preparation. Click Here to Download NCERT Solutions for Class 10 Maths chapter 4 Quadratic Equations.

NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations (Hindi Medium) Ex 4.1

NCERT Solutions for class 10 Maths chapter 4 Exercise 4.1
NCERT Solutions for class 10 Maths chapter 4 Exercise 4.1 in English medium
Class 10 Maths chapter 4 exercise 4.1 in english PDF
NCERT Solutions for class 10 Maths chapter 4 Exercise 4.1 in Hindi medium
NCERT Solutions for class 10 Maths chapter 4 Exercise 4.1 in Hindi pdf
class 10 maths chapter 4 ex. 4.1 in hindi
NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.1 Quadratic Equations
NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.1 in English PDF
class 10 maths chapter 4 exercise 4.1 in Hindi

Class 10 Maths Quadratic Equations Mind Map

Quadratic Equation

Standard form of the quadratic equation in the variable x is an equation of the form ax2 + bx + c = 0, where a, b, c are real numbers and a ≠ 0.
Any equation of the form P(x) = 0, Where P(x) is a polynomial of degree 2, is a quadratic equation.

Zero(es)/Root(s) of Quadratic Equation

A real number α is said to be a root of the quadratic equation ax2 + bx + c = 0, a ≠ 0 if aα2 + bα + c = 0.
We can say that x = α, is a solution of the quadratic equation or that α satisfies the quadratic equation.
The zeroes of the quadratic polynomial ax2 + bx + c = 0 and the roots of the equation ax2 + bx + c = 0 are same. A quadratic equation has atmost two roots/zeroes.

Relation Between Zeroes and Co-efficient of a Quadratic Equation

If α and β are zeroes of the quadratic equation ax2 + bx + c = 0, where a, b, c are real numbers and a ≠ 0 then
NCERT Solutions For Class 10 Maths Chapter 4 Quadratic Equations Ex 4.1 Q1

Methods of Solving Quadratic Equation

Following are the methods which are used to solve quadratic equations:

(i) Factorisation
(ii) Completing the square
(iii) Quadratic Formula

Methods of Factorisation

In this method we find the roots of a quadratic equation (ax2 + bx + c = 0) by factorising LHS it into two linear factors and equating each factor to zero, e.g.,
6x2 – x – 2 = 0
⇒ 6x2 + 3x – 4x – 2 = 0 …(i)
⇒ 3x (2x + 1) – 2(2x + 1) = 0
⇒ (3x — 2) (2x + 1) = 0
⇒ 3x – 2 = 0 or 2x + 1 = 0
NCERT Solutions For Class 10 Maths Chapter 4 Quadratic Equations Ex 4.1 Q2
Necessary Condition : Product of 1st and last terms of eq. (i) should be equal to product of 2nd and 3rd terms of the same equation.

Method of Completing the Square

This is the method of converting L.H.S. of a quadratic equation which is not a perfect square into the sum or difference of a perfect square and a constant by adding and subtracting the suitable constant terms. E.g,
(1) x2 + 4x – 5 = 0
⇒ x2 + 2(2)(x) -5 = 0
⇒ x2 + 2(2)(x) + (2)2 – (2)2 – 5 = 0
⇒ (x + 2)2 – 4 – 5 = 0
⇒ (x + 2)2 – 9 = 0
⇒ x + 2 = ± 3
⇒ x = —5, 1
(2) 3x2 – 5x + 2 = 0
NCERT Solutions For Class 10 Maths Chapter 4 Quadratic Equations Ex 4.1 Q3

Quadratic Formula

Consider a quadratic equation: ax2 + bx + c = 0.
If b2 – 4ac ≥ 0, then the roots of the above equation are given by:
NCERT Solutions For Class 10 Maths Chapter 4 Quadratic Equations Ex 4.1 Q4

Nature of Roots

For quadratic equation ax2 + bx + c = 0
(a ≠ 0), value of (b2 – 4ac) is called discriminant of the equation and denoted as D.
D = b2 – 4ac
Discriminant is very important in finding nature of the roots.
(i) If D = 0, then roots are real and equal.
(ii) If D > 0, then roots are real and unequal
(iii) If D < 0, then roots are not real.

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