Maths project abhi.pptx [autosaved]

BY:-Abhishek.T.Raja

nClass:-10th DRoll no.:-33

Polynomials

CONTENTS1. Introduction.

2. Zeroes of polynomials.

3. Relation between coefficients and zeroes of

polynomials.

4. Division Algorithm for Polynomials.

5. Summary.

1.INTRODUCTION A polynomial is an expression constructed

from variables and constants using only the

operations of addition, subtraction, multiplication,

and non-negative integer exponents . However,

the division by a constant is allowed, because

the multiplicative inverse of a non-zero constant is

also a constant.For eg:-2x+7y, 3a+b, x+6

Types of polynomial on the basis of degree The polynomial which has one degree is

called linear polynomial. for eg:-2x+3, 7x+9,

9x+13.

The polynomial which has two degree is called

quadratic polynomial. for eg:-2x2+3, 7x2+9.

The polynomial which has three degree is called

cubic polynomial. For eg:-x3+8, 3x3+45.

2. Zeroes of polynomialsDefinition:- Take an equation 2x2+6x+4. Do it’s middle term splitting. = 2x2+(2+4)x+4 = 2x2+2x+4x+4 Take common in this equation = 2x(x+1)+4(x+1) Take common = (2x+4)(x+1)

Let, 2x+4=0Then, 2x=-4 x=-4/2 x=-2Let, x+1=0 x=-1So ,we have two zeroes that is -4, -1.By this we can conclude that the number

replacing variable giving zero on doing mathematical operation is called zeroes of polynomial.

We represent linear equation in the form ax2+by+c.Relation between coefficient and zeroes are:-a) Sum of zeroes of polynomial=-c/ab) Product of zeroes of polynomial=b/aIf one zero is α and second is β.a) α+ β=-c/ab) αβ=b/aSo this is the relation between coefficients and

zeroes of polynomial.

3. Relation between coefficients and zeroes of

polynomials.

4. Division Algorithm for polynomial Division algorithm is a method by which we

can divide any two polynomial. Example :-

5)Summary1) Polynomials of degree 1, 2 & 3 are called

linear, quadric and cubic polynomials respectively.2) A quadric polynomial can have at most two

zeros and a cubic polynomial can have three zeros.3) If we are given with the sum and product of

zeros we can find the polynomial by the following formula:

K[x2+(sum of zeros)x+(Product of zeros)]

4) If two zeros of a polynomial are given then we can find the third zero by the following steps:

Convert the zeros into factors of the polynomial

Make a combined factor by multiplying the two

factors Now divide the polynomial by the combined

factor Write the quotient separately Do middle term splitting

By this process, we can find the third zero of the polynomial.

Thank you and bye bye

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