Zero of polynomial explained with examples

Know what is the meaning of zero of polynomial? Also learn how to find the zero of a polynomial. In polynomials concept, this is the easiest one which we can understand easily. Only you need to how to simply a given equation.

Zero of polynomial explained with examples

Hope that you know what is a polynomial? We know that in polynomials, we have different types of polynomials based on their degree like linear, quadratic, cubic and bi-quadratic polynomials. For all these polynomials, know totally how many zeros they have and how to find them. First thing you have to do is “to understand the definition and meaning of zero of polynomial” which is very very important. So for this, just see the below given definition and also the example.

The definition of zero of polynomial:

Zero of polynomial definitions as follows “value of a variable which makes the polynomial to become zero is called as zero of polynomial”.


If 4y+3 is a polynomial then zero of this polynomial is \frac { -3 }{ 4 } . If we substitute \frac { -3 }{ 4 } in the place of “y” then the given polynomial 4y+8 becomes zero.


Number of zeros for a linear polynomial is “1”, for a quadratic polynomial is “2”, for a cubic polynomial is “3”and for a bi-quadratic polynomial is “4”.

Generally linear polynomial is represented as ax+b (where “a” is not equal to zero) and its zero of polynomial is given by \frac { -b }{ a } .

Quadratic polynomial, if we make it equal o zero, then it becomes the quadratic equation. So we need to simplify quadratic equation and find roots. For simplifying, we can use formula method or by factorization method.

Cubic and bi-quadratic polynomials also we need to do simplification by a suitable method i.e. by synthetic division or by trial and error method to find the roots, nothing but zeros.

Procedure for finding zero of a polynomial:

Step 1:

Given polynomial make it equal to zero. Suppose 7x+11 is a given polynomial then write it as 7x+11 =0.

Step 2:

Now solve the equation, you will get the values o the variable. These values are zeros of polynomial. In this example x is \frac { -11 }{ 7 } .

Example :

What is the zero of polynomial of 9a-5.


First make it equal to zero, so we get 9a-5 =0, which is a linear equation in terms of “a”.

Now simply and get “a” value.

9a-5 =0

9a = 5

a = \frac { 5 }{ 9 } .

Therefore, \frac { 5 }{ 9 } is the zero of polynomial.

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