Relationship between Zeros and coefficients of a Polynomial
zeros of a polynomial : A real number is called a zero of the polynomial
.
If “, then by factor theorem
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,
Let be a linear polynomial,
then.
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 are factors of
, where
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 and
Let ,
be the zeros of the cubic polynomial
Then ,
are factors of
, 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