• Skip to main content
  • Skip to secondary menu
  • Skip to primary sidebar
  • Skip to footer
  • RBSE Model Papers
    • RBSE Class 12th Board Model Papers 2022
    • RBSE Class 10th Board Model Papers 2022
    • RBSE Class 8th Board Model Papers 2022
    • RBSE Class 5th Board Model Papers 2022
  • RBSE Books
  • RBSE Solutions for Class 10
    • RBSE Solutions for Class 10 Maths
    • RBSE Solutions for Class 10 Science
    • RBSE Solutions for Class 10 Social Science
    • RBSE Solutions for Class 10 English First Flight & Footprints without Feet
    • RBSE Solutions for Class 10 Hindi
    • RBSE Solutions for Class 10 Sanskrit
    • RBSE Solutions for Class 10 Rajasthan Adhyayan
    • RBSE Solutions for Class 10 Physical Education
  • RBSE Solutions for Class 9
    • RBSE Solutions for Class 9 Maths
    • RBSE Solutions for Class 9 Science
    • RBSE Solutions for Class 9 Social Science
    • RBSE Solutions for Class 9 English
    • RBSE Solutions for Class 9 Hindi
    • RBSE Solutions for Class 9 Sanskrit
    • RBSE Solutions for Class 9 Rajasthan Adhyayan
    • RBSE Solutions for Class 9 Physical Education
    • RBSE Solutions for Class 9 Information Technology
  • RBSE Solutions for Class 8
    • RBSE Solutions for Class 8 Maths
    • RBSE Solutions for Class 8 Science
    • RBSE Solutions for Class 8 Social Science
    • RBSE Solutions for Class 8 English
    • RBSE Solutions for Class 8 Hindi
    • RBSE Solutions for Class 8 Sanskrit
    • RBSE Solutions

RBSE Solutions

Rajasthan Board Textbook Solutions for Class 5, 6, 7, 8, 9, 10, 11 and 12

  • RBSE Solutions for Class 7
    • RBSE Solutions for Class 7 Maths
    • RBSE Solutions for Class 7 Science
    • RBSE Solutions for Class 7 Social Science
    • RBSE Solutions for Class 7 English
    • RBSE Solutions for Class 7 Hindi
    • RBSE Solutions for Class 7 Sanskrit
  • RBSE Solutions for Class 6
    • RBSE Solutions for Class 6 Maths
    • RBSE Solutions for Class 6 Science
    • RBSE Solutions for Class 6 Social Science
    • RBSE Solutions for Class 6 English
    • RBSE Solutions for Class 6 Hindi
    • RBSE Solutions for Class 6 Sanskrit
  • RBSE Solutions for Class 5
    • RBSE Solutions for Class 5 Maths
    • RBSE Solutions for Class 5 Environmental Studies
    • RBSE Solutions for Class 5 English
    • RBSE Solutions for Class 5 Hindi
  • RBSE Solutions Class 12
    • RBSE Solutions for Class 12 Maths
    • RBSE Solutions for Class 12 Physics
    • RBSE Solutions for Class 12 Chemistry
    • RBSE Solutions for Class 12 Biology
    • RBSE Solutions for Class 12 English
    • RBSE Solutions for Class 12 Hindi
    • RBSE Solutions for Class 12 Sanskrit
  • RBSE Class 11

RBSE Class 10 Maths Notes Chapter 2 Polynomials

April 12, 2022 by Prasanna Leave a Comment

These comprehensive RBSE Class 10 Maths Notes Chapter 2 Polynomials will give a brief overview of all the concepts.

RBSE Class 10 Maths Chapter 2 Notes Polynomials

Important Points

1. In a polynomial p(x) of any variable x, the highest power of x is called the degree of the polynomial. For example: 5x + 2 is a polynomial of degree 1 in variable 2y2 – 3y + 4 is a polynomial of degree 2 in variable y. x3 – 6a2 + x + 9 is a polynomial of degree 3 in variable x.

2. A polynomial of degree 1 is called a linear polynomial, a polynomial of degree 2 is called a quadratic polynomial, and a polynomial of degree 3 is called a cubic polynomial.

RBSE Class 10 Maths Notes Chapter 2 Polynomials

3. A quadratic polynomial in variable x is of the form ax2 + bx + c where a, b, c are real numbers and a≠0

4. Value of a polynomial – If p(x) is any polynomial in x and k is any real number, then the value obtained by replacing x by k in p(x), is called the value of p(x) at x = k and it is devoted by p(k).

5. Zero of a polynomial—A real number k is said to be a zero of a polynomial p(x), if p(k) = 0. In general,
⇒ p(x) =   ax + b
or p(k) =  ak + b
or p(k) =   0
⇒ ak + b = 0 or k    =  -b/a.

6. The zeroes of polynomial are the x-coordinates of the points, where the graph of y = p(x) Intersect the x-axis.

7. In fact, for any quadratic polynomial ax2 + bx + c, a * 0, the graph of the corresponding equation y = ax2 + bx + c has one of the two shapes either open upwards like ∪ or open downwords like ∩ depending upon whether
a > 0 or a < 0 (These curves are called parabolas.)

8. A quadratic polynomial can have at most 2 zeroes and a cubic polynomial can have at most 3 zeroes.

Note — In general, given a polynomial p(x) of degree n, the graph of y = p(x) intersects the x-axis at atmost n points. Therefore, a polynomial p(x) of degree n has atmost n zeroes.

RBSE Class 10 Maths Notes Chapter 2 Polynomials

9. If α and β are the zeroes of a quadratic polynomial ax2 + bx + c, then
α + β = – \(\frac{b}{a}=\frac{-(\text { Coefficient of } x)}{\text { Coefficient of } x^{2}}\)

α β = \(\frac{c}{a}=\frac{\text { Constant term }}{\text { Coefficient of } x^{2}}\)

10. If α, β, γ are the zeroes of the cubic polynomial ax’ + bx2 + cx + d = 0, then
α + β + γ = \(\frac{-b}{a}=\frac{-\left(\text { Coefficient of } x^{2}\right)}{\text { Coefficient of } x^{3}}\)

αβ + βγ+ γα  = \(\frac{c}{a}=\frac{\text { Coefficient of } x}{\text { Coefficient of } x^{3}}\)

and αβγ = \(\frac{-d}{a}=\frac{-\text { Constant term }}{\text { Coefficient of } x^{3}}\)

RBSE Class 10 Maths Notes Chapter 2 Polynomials

11. According to Euclid’s Division Algorithm, for given polynomial p(x) and non-zero polynomial g(x), these exist two polynomials q(x) and r(x) such that.
p(x) = g(x) q(x) + r(x),
where   r(x) = 0 or degree r(x) < degree g(x)

 

Share this:

  • Click to share on WhatsApp (Opens in new window)
  • Click to share on Twitter (Opens in new window)
  • Click to share on Facebook (Opens in new window)

Related

Filed Under: RBSE Notes

Reader Interactions

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Primary Sidebar

Recent Posts

  • RBSE Solutions for Class 6 Maths Chapter 6 Decimal Numbers Additional Questions
  • RBSE Solutions for Class 11 Psychology in Hindi Medium & English Medium
  • RBSE Solutions for Class 11 Geography in Hindi Medium & English Medium
  • RBSE Solutions for Class 3 Hindi
  • RBSE Solutions for Class 3 English Let’s Learn English
  • RBSE Solutions for Class 3 EVS पर्यावरण अध्ययन अपना परिवेश in Hindi Medium & English Medium
  • RBSE Solutions for Class 3 Maths in Hindi Medium & English Medium
  • RBSE Solutions for Class 3 in Hindi Medium & English Medium
  • RBSE Solutions for Class 4 Hindi
  • RBSE Solutions for Class 4 English Let’s Learn English
  • RBSE Solutions for Class 4 EVS पर्यावरण अध्ययन अपना परिवेश in Hindi Medium & English Medium

Footer

RBSE Solutions for Class 12
RBSE Solutions for Class 11
RBSE Solutions for Class 10
RBSE Solutions for Class 9
RBSE Solutions for Class 8
RBSE Solutions for Class 7
RBSE Solutions for Class 6
RBSE Solutions for Class 5
RBSE Solutions for Class 12 Maths
RBSE Solutions for Class 11 Maths
RBSE Solutions for Class 10 Maths
RBSE Solutions for Class 9 Maths
RBSE Solutions for Class 8 Maths
RBSE Solutions for Class 7 Maths
RBSE Solutions for Class 6 Maths
RBSE Solutions for Class 5 Maths
RBSE Class 11 Political Science Notes
RBSE Class 11 Geography Notes
RBSE Class 11 History Notes

Copyright © 2023 RBSE Solutions