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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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Also, students can refer,
- NCERT Solutions for Class 10 Maths Chapter 2 Polynomials
- NCERT Exemplar Solutions for Class 10 Maths Chapter 2 Polynomials
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
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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.
Graph of Quadratic Polynomial-
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/a Product of zeroes (αβ)=c/a |
Cubic | ax3+bx2+cx+d, a≠0 | 3 | Sum of zeroes(α + β+γ )=-b/a Product of zeroes taken two at a time(α β+ βγ+αγ )=c/a Product 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.
In offline mode, Class 10 Math’s chapter 2 notes pdf download/Polynomials Class 10 notes pdf download can be referred.
Class 10 Chapter Wise Notes
NCERT Solutions of Cass 10 Subject Wise
NCERT Class 10 Exemplar Solutions for Other Subjects:
Frequently Asked Questions (FAQs)
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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