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

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

If “” is a zero of a polynomial , then by factor theorem is a factor of a given polynomial. The relation between the zeros and the coefficients of a polynomial is given below.

**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, is a variable, “a” and “b**” **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 be the zeros of the quadratic polynomial .

Then and are factors of ., where is a constant.

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

**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 and and are constants.

Let , and be the zeros of the cubic polynomial .

Then , and are factors of .

, for some constant .

=

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

If , and be the zeros of the cubic polynomial , then

(i) (ii) (iii)

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

.

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

download link: polynomial worksheet