# Free NCERT Class 10 Maths Chapter 2 Notes - Download PDF

Edited By Ramraj Saini | Updated on Feb 12, 2024 06:27 PM IST

Polynomials Class 10th Notes are provided here. These NCERT notes are created by an expert team at careers360 considering the need of students. these are helpful to revise quickly all the concepts discussed in this chapter. Also these notes includes shorts tricks, tips and formulas to solve the problems. Polynomials in the NCERT chapter deals with algebraic equations. It can be a quadratic, linear, or cubic equation. The NCERT Class 10 Maths chapter 2 notes covers a brief outline of the chapter Polynomial. The main topics covered Polynomials Class 10 notes, give you different types of polynomials. Class 10 Math’s chapter 2 notes also include the important formulas in the chapter. These topics can also be downloaded from Polynomial Class 10 notes pdf download.

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## Polynomials Class 10 Notes:

A polynomial is an expression that contains constants, variables, and exponents.

The mathematical form is-

Degree of Polynomials

Consider the polynomial 3x2. Here, 3 is the leading coefficient and 2 is the degree.

Let F(y) is a polynomial in y, then the highest power of y in the F(y) will be the degree of polynomial F(y).

Types of Polynomial according to their Degrees

 Type of polynomial Degree Form Constant 0 F(x) = a Linear 1 F(x) = ax + b Quadratic 2 F(x) = ax2 + bx + c Cubic 3 F(x) = ax3 + bx2+ cx + d

Value of Polynomial

Let f(y) be a polynomial in y and α be any real number, then the value calculated after putting the value y = α in f(y) is the final value of f(y) at y = α. This shows that f(y) at y = α is represented by f(α).

Zero of a Polynomial

Zero of a polynomial f(x) is all the values of x that make the polynomial value zero.

### Geometrical Meaning of the Zeroes of a Polynomial

The coordinates of the x-axis of a point at which the graph of the polynomial divides the axis are called Zeroes of the polynomial.

Graph of a Linear Polynomial

Graph of a linear polynomial is a straight line that intersects the x-axis at one point only, therefore a linear equation has 1 degree.

Case 1: The two points shown are the two zeroes of the quadratic equation when the graph cuts the x-axis at those particular points.

Case 2: A point is called the zero of that quadratic equation when the graph cuts the x-axis at a single point and the equation will be a perfect square.

Case 3: When the graph does not divide the x-axis at any point, then the graph is either completely above the x-axis or below the x-axis. At that condition, the quadratic equation has no zeros, because the equation does not divide the x-axis at any point.

## Relationship Between Zeroes and Coefficients of a Polynomial

Let α and β are zeroes of quadratic polynomial and α, β and γ are zeroes of a cubic polynomial-

 Polynomial Form Zeros Relationship between zeroes and coefficients of a polynomial Quadratic ax2+bx+c, a≠0 2 Sum of zeroes(α + β)=-b/aProduct of zeroes (αβ)=c/a Cubic ax3+bx2+cx+d, a≠0 3 Sum of zeroes(α + β+γ )=-b/aProduct of zeroes taken two at a time(α β+ βγ+αγ )=c/aProduct of zeroes(αβγ )=-d/a

## Division Algorithm for Polynomial

If f(x) and h(x) are any two polynomials with h(x) ≠ 0, then we can easily find polynomials g(x) and j(x) such that

f(x) = h(x) × g(x) + j(x),

where g(x) not equal to 0 or degree of g(x) < degree of h(x).

g(x) is diviso, h(x) quotient r and r(x) is reminder

## Significance of NCERT Class 10 Math’s Chapter 2 Notes-

Polynomials Class 10 notes will give a detailed overview of the chapter and get a sense of the main topics discussed.

This NCERT Class 10 Maths chapter 2 notes will help to understand the formulas, statements, rules in detail.

## Class 10 Chapter Wise Notes

 NCERT Class 10 Maths Chapter 1 Notes NCERT Class 10 Maths Chapter 2 Notes NCERT Class 10 Maths Chapter 3 Notes NCERT Class 10 Maths Chapter 4 Notes NCERT Class 10 Maths Chapter 5 Notes NCERT Class 10 Maths Chapter 6 Notes NCERT Class 10 Maths Chapter 7 Notes NCERT Class 10 Maths Chapter 8 Notes NCERT Class 10 Maths Chapter 9 Notes NCERT Class 10 Maths Chapter 10 Notes NCERT Class 10 Maths Chapter 11 Notes NCERT Class 10 Maths Chapter 12 Notes NCERT Class 10 Maths Chapter 13 Notes NCERT Class 10 Maths Chapter 14 Notes NCERT Class 10 Maths Chapter 15 Notes

## NCERT Class 10 Exemplar Solutions for Other Subjects:

 NCERT Books for Class 10 NCERT Syllabus for Class 10

1. What are the types of polynomials discussed in Class 10 Math’s chapter 2 notes?

Linear polynomial, zero polynomial, quadratic polynomial and cubic polynomial.

2. What is the weightage of the topics in Class 10 Polynomials notes ?

Students can expect 4 to 8 marks questions from the notes for Class 10 Math’s chapter 2.

3. What are the zeros of a polynomial?

It is given in Class 10 Math’s chapter 2 notes

if the value of f(y) at y = k is 0, that is f (k) = 0 then y = k will be the zero of that polynomial f(y).

4. What is the value of a polynomial?

Let f(y) be a polynomial in y and α be any real number, then the value calculated after putting the value y = α in f(y) is the final value of f(y) at y = α. This shows that f(y) at y = α is represented by f(α).

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A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

 Option 1) Option 2) Option 3) Option 4)

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

 Option 1) 2.45×10−3 kg Option 2)  6.45×10−3 kg Option 3)  9.89×10−3 kg Option 4) 12.89×10−3 kg

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

 Option 1) Option 2) Option 3) Option 4)

A particle is projected at 600   to the horizontal with a kinetic energy . The kinetic energy at the highest point

 Option 1) Option 2) Option 3) Option 4)

In the reaction,

 Option 1)   at STP  is produced for every mole   consumed Option 2)   is consumed for ever      produced Option 3) is produced regardless of temperature and pressure for every mole Al that reacts Option 4) at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, will contain 0.25 mole of oxygen atoms?

 Option 1) 0.02 Option 2) 3.125 × 10-2 Option 3) 1.25 × 10-2 Option 4) 2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

 Option 1) decrease twice Option 2) increase two fold Option 3) remain unchanged Option 4) be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

 Option 1) Molality Option 2) Weight fraction of solute Option 3) Fraction of solute present in water Option 4) Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

 Option 1) twice that in 60 g carbon Option 2) 6.023 × 1022 Option 3) half that in 8 g He Option 4) 558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

 Option 1) less than 3 Option 2) more than 3 but less than 6 Option 3) more than 6 but less than 9 Option 4) more than 9