BlogNCERTNCERT 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

Board CBSE
Textbook NCERT
Class Class 10
Subject Maths
Chapter Chapter 4
Chapter Name Quadratic Equations
Exercise Ex 4.1
Number of Questions Solved 2
Category NCERT Solutions

Ex 4.1 Class 10 Maths Question 1.

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    Check whether the following are quadratic equations:

    1. (x+ 1)2=2(x-3)
    2. x – 2x = (- 2) (3-x)
    3. (x – 2) (x + 1) = (x – 1) (x + 3)
    4. (x – 3) (2x + 1) = x (x + 5)
    5. (2x – 1) (x – 3) = (x + 5) (x – 1)
    6. x2 + 3x + 1 = (x – 2)2
    7. (x + 2)3 = 2x(x2 – 1)
    8. 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

    Ex 4.1 Class 10 Maths Question 2.

    Represent the following situations in the form of quadratic equations:

    1. The area of a rectangular plot is 528 m2. The length of the plot (in meters) is one more than twice its breadth. We need to find the length and breadth of the plot.
    2. The product of two consecutive positive integers is 306. We need to find the integers.
    3. Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We want to find Rohan’s present age.
    4. A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, 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

    NCERT Solutions 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 10 Maths chapter 4 Exercise 4.1
    NCERT Solutions for 10 Maths chapter 4 Exercise 4.1 in English medium
    Class 10 Maths chapter 4 exercise 4.1 in english PDF
    NCERT Solutions for 10 Maths chapter 4 Exercise 4.1 in Hindi medium
    NCERT Solutions for 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

    The standard form of the quadratic equation in the variable x is an equation of ax2 + bx + c = 0, where a, b, and 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, and 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 the 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 that 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 the discriminant of the equation and denoted as D.
    D = b2 – 4ac
    The discriminant is very important in finding the nature of the roots.

    1. If D = 0, then roots are real and equal.
    2. If D > 0, then roots are real and unequal
    3. If D < 0, then roots are not real.
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