Page 1 - Lesson Note-Zeroes of a Polynomial Ch-2

SAI International School
CLASS - IX

Mathematics
CHAPTER-2: ZEROES OF A POLYNOMIAL Lesson Notes-2

Sub Topic:

Zero of a Polynomial:
It is the value of the variable for which the value of the polynomial will be equal to
zero.
If p(x) is a polynomial then the number ‘a’ will be the zero of the polynomials with
p(a) = 0. We can find the zero of the polynomials by equating it to zero.
For a polynomial p(x), if p(a) =0, then ‘a’ is called as the Zero of the polynomial.
Example: 1

Given polynomial is p(x) = x - 4

To find the zero of the polynomial, we will equate it to zero.

x - 4 = 0

x = 4
p(4) = x – 4 = 4 – 4 = 0

This shows that if we place 4 in place of x, we got the value of the polynomial as
zero. So, 4 is the zero of this polynomial. And also, we are getting the value 4 by
equating the polynomial by 0.

So, 4 is the zero of the polynomial or root of the polynomial.

Example; 2

2
Let x =4 so x= 2 and x= - 2 are the zeroes of the polynomial.
VERIFICATION
2
2
For x=2 , x – 4 = 2 - 4 =0 (Verified)
2
2
For x= -2 , x – 4 = (-2) - 4 =0 (Verified)
HOW TO FIND ZEROES OF A POLYNOMIAL?

Consider the polynomial = 0

p(x)=0

Zero of a linear polynomial of one variable
Let p(x) = a x + b , where a≠ 0 .

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