maths class 9polynomials

56 %
44 %
Information about maths class 9polynomials

Published on April 10, 2013

Author: shaurya192


PowerPoint Presentation: Maths is my favourite subject I love maths MATHS PROJECT Polynomials Shaurya Chopra PowerPoint Presentation: CONTENTS 1.INTRODUCTION 2.GEOMETRICAL MEANING OF ZEROES OF THE POLYNOMIAL 3.RELATION BETWEEN ZEROES AND COEFFICIENTS OF A POLYNOMIAL 4.DIVISION ALGORITHM FOR POLYNOMIAL 5.SUMMARY 6.QUESTIONS AND EXERCISE PowerPoint Presentation: ACKNOWLEDGEMENT The national curriculum framework such that children's life at school must be linked to their life outside the school. this principle marks a de portable use from the legacy of bookish learning and thus the students have been given provisions to preface some project reports on certain subjects. I express my hearty gratitude to CBSE for providing such an interesting and board scope topic for our project. I am really thankful to our respected subject teacher Ms.Nivedita Saxena who helped us in a passive way. I would also like to thank my parents and my friends for their help, encouragement and blessings. 1234567891011121314151617181920 PowerPoint Presentation: POLYNOMIALS 2x 2 + 3x = 5 2x 2 + 3x= 9 x 3 – 3x 2 + x +1 = 0 4y 3 - 4y 2 + 5y + 8 = 0 9x 2 + 9y + 8 =0 PowerPoint Presentation: INTRODUCTION In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative, whole-number exponents. Polynomials appear in a wide variety of areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated problems in the sciences; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; they are used in calculus and numerical analysis to approximate other functions. PowerPoint Presentation: RECAPTULATION PowerPoint Presentation: POLYNOMIAL Let x be a variable n, be a positive integer and as, a 1 ,a 2 ,….a n be constants (real nos.) Then, f(x) = a n x n + a n-1 x n-1 +….+a 1 x+x o a n x n ,a n-1 x n-1 ,….a 1 x and a o are known as the terms of the polynomial. a n ,a n-1 ,a n-2 ,….a 1 and a o are their coefficients . For example : p(x) = 3x – 2 is a polynomial in variable x. q(x) = 3y 2 – 2y + 4 is a polynomial in variable y. f(u) = 1/2u 3 – 3u 2 + 2u – 4 is a polynomial in variable u. NOTE : 2x 2 – 3√x + 5, 1/x 2 – 2x +5 , 2x 3 – 3/x +4 are not polynomials . PowerPoint Presentation: The exponent of the highest degree term in a polynomial is known as its degree . For example : f(x) = 3x + ½ is a polynomial in the variable x of degree 1. g(y) = 2y 2 – 3/2y + 7 is a polynomial in the variable y of degree 2. p(x) = 5x 3 – 3x 2 + x – 1/√2 is a polynomial in the variable x of degree 3. q(u) = 9u 5 – 2/3u 4 + u 2 – ½ is a polynomial in the variable u of degree 5. PowerPoint Presentation: CONSTANT Polynomial A polynomial of degree zero is called a constant polynomial. LINEAR polynomial A polynomial of degree one is called a linear polynomial For example: f(x) = 7, g(x) = -3/2, h(x) = 2 are constant polynomials. The degree of constant polynomials is not defined. For example: p(x) = 4x – 3, q(x) = 3y are linear polynomials. Any linear polynomial is in the form ax + b, where a, b are real nos. and a ≠ 0. It may be a monomial or a binomial. F(x) = 2x – 3 is binomial whereas g (x) = 7x is monomial. PowerPoint Presentation: A polynomial of degree two is called a quadratic polynomial. f(x) = √3x 2 – 4/3x + ½, q(w) = 2/3w 2 + 4 are quadratic polynomials with real coefficients. Any quadratic is always in the form f(x) = ax 2 + bx +c where a,b,c are real nos . and a ≠ 0. QUADRATIC POLYNOMIAL CUBIC POLYNOMIAL A polynomial of degree three is called a cubic polynomial. f(x) = 9/5x 3 – 2x 2 + 7/3x _1/5 is a cubic polynomial in variable x. Any cubic polynomial is always in the form f(x = ax3 + bx2 +cx + d where a,b,c,d are real nos. PowerPoint Presentation: VALUE OF POLYNOMIAL ZERO OF THE POLYNOMIAL A real no. x is a zero of the polynomial f(x),is f(x) = 0 Finding a zero of the polynomial means solving polynomial equation f(x) = 0. If f(x) is a polynomial and y is any real no. then real no. obtained by replacing x by y in f(x) is called the value of f(x) at x = y and is denoted by f(x). Value of f(x) at x = 1 f(x) = 2x 2 – 3x – 2 f(1) = 2(1) 2 – 3 x 1 – 2 = 2 – 3 – 2 = -3 Zero of the polynomial f(x) = x 2 + 7x +12 f(x) = 0 x2 + 7x + 12 = 0 (x + 4) (x + 3) = 0 x + 4 = 0 or, x + 3 = 0 x = -4 , -3 PowerPoint Presentation: GRAPHS OF THE POLYNOMIALS An nth degree polynomial can have at most n real zeroes. no. of real zeros of a polynomial is less than or equal to degree of the polynomial PowerPoint Presentation: GENERAL SHAPES OF POLYNOMIAL FUNCTIONS f(x) = 3 CONSTANT FUNCTION DEGREE = 0 MAX. ZEROES = 0 PowerPoint Presentation: GENERAL SHAPES OF POLYNOMIAL FUNCTIONS f(x) = x + 2 LINEAR FUNCTION DEGREE =1 MAX. ZEROES = 1 PowerPoint Presentation: GENERAL SHAPES OF POLYNOMIAL FUNCTIONS f(x) = x 2 + 3x + 2 QUADRATIC FUNCTION DEGREE = 2 MAX. ZEROES = 2 PowerPoint Presentation: GENERAL SHAPES OF POLYNOMIAL FUNCTIONS f(x) = x 3 + 4x 2 + 2 CUBIC FUNCTION DEGREE = 3 MAX. ZEROES = 3 PowerPoint Presentation: RELATIONSHIP B/W ZEROES AND COEFFICIENTS OF A POLYNOMIAL QUADRATIC A + B = - coefficient of x Coefficient of x 2 = - b a AB = constant term Coefficient of x 2 = c a PowerPoint Presentation: RELATIONSHIP B/W ZEROES AND COEFFICIENTS OF POLYNOMIALS CUBIC A + B + C = -Coefficient of x 2 = -b Coefficient of x 3 a AB + BC + CA = Coefficient of x = c Coefficient of x 3 a ABC = - Constant term = d Coefficient of x 3 a PowerPoint Presentation: RELATIONSIPS ON VERYFYING THE RELATIONSHIP BETWEEN THE ZEROES AND COEFFICIENTS ON FINDING THE VALUES OF EXPRESSIONS INVOLVING ZEROES OF QUADRATIC POLYNOMIAL ON FINDING AN UNKNOWN WHEN A RELATION BETWEEEN ZEROES AND COEFFICIENTS ARE GIVEN. OF ITS A QUADRATIC POLYNOMIAL WHEN THE SUM AND PRODUCT OF ITS ZEROES ARE GIVEN. PowerPoint Presentation: DIVISION ALGORITHM PowerPoint Presentation: If f(x) and g(x) are any two polynomials with g(x) ≠ 0,then we can always find polynomials q(x), and r(x) such that : F(x) = q(x) g(x) + r(x), Where r(x) = 0 or degree r(x) < degree g(x) ON VERYFYING THE DIVISION ALGORITHM FOR POLYNOMIALS. ON FINDING THE QUOTIENT AND REMAINDER USING DIVISION ALGORITHM. ON CHECKING WHETHER A GIVEN POLYNOMIAL IS A FACTOR OF THE OTHER POLYNIMIAL BY APPLYING THEDIVISION ALGORITHM ON FINDING THE REMAINING ZEROES OF A POLYNOMIAL WHEN SOME OF ITS ZEROES ARE GIVEN. PowerPoint Presentation: made by : Shaurya Chopra cLaSs : 9 - D Amity international sCHool

Add a comment

Related presentations

Related pages

Class 9 CBSE Maths Polynomials Factorization of ...

Study Material for Factorization of Polynomials Using Algebraic Identities of Polynomials of Maths of Class IX of CBSE Board. Watch video ...
Read more

CBSE Class 9 Maths Polynomials Exercise 2.5

CBSE Class 9 Maths Polynomials Exercise 2.5 ... very very thanks and now im good in maths thanks very very ... Class 10- Maths - SA1 Paper ...
Read more

Rs Aggarwal Class 9polynomials -

On this page you can read or download Rs Aggarwal Class 9polynomials in PDF format.
Read more

Help me to make 9th class maths presentation (PPT ...

Best Answer: If u want to make 9th class presentation simply open ms office power point and type what u want u can also give it animations ...
Read more