**Relationship between Zeros and coefficients of a Polynomial**

**zeros of a polynomial :** A real number is called a zero of the polynomial

If “

**Linear Polynomial:**

The linear polynomial is an expression , in which the degree of the polynomial is 1 . The general form of a linear polynomial is **.** Here,

**”**are constant.

**Let ** be a linear polynomial,

then

**means**

**.**

** **

**So =**

**.**

**Quadratic polynomial****:**A polynomial of degree 2 is called a quadratic polynomial. A quadratic polynomial in one variable will have at most tree terms. Any quadratic polynomial in will be of the form

Let and

Then

On comparing coefficients of like powers of

**sum of zeros = – **

**product of zeros = **

**Cubic polynomial : **** **A polynomial of degree 3 is called cubic polynomials. Any cubic polynomial can have at most 4 terms. Cubic polynomial can be written in the form

Let ,

Then ,

, for some constant

=

On comparing coefficients of like powers of on both sides, we get

(i) (ii)

Similarly, If α , β, γ, δ are roots of the equation

Some practice questions based on polynomial are given in the following worksheet.

download link: polynomial worksheet