1. BY:-
Abhishek.T.Rajan
Class:-10th D
Roll no.:-33
Polynomials

2. CONTENTS
1. Introduction.
2. Zeroes of polynomials.
3. Relation between coefficients and zeroes of
polynomials.
4. Division Algorithm for Polynomials.
5. Summary.

3. 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

4. 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.

5. 2. Zeroes of polynomials
Definition:- 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)

6. Let, 2x+4=0
Then, 2x=-4
x=-4/2
x=-2
Let, x+1=0
x=-1
So ,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.

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

8. 4. Division Algorithm for polynomial
Division algorithm is a method by which we can divide
any two polynomial. Example :-

11. 5)Summary
1) 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)]

12. 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.