Relationship between Zeros and Coefficients of a Polynomial
We know that zeros of any polynomial are the points where the graph of the polynomial cuts the x-axis. These zeros can also be found using the coefficients of different terms in a polynomial. Let’s look at the relationship between the zeros and coefficients of the polynomials for various types of polynomials.
The following image shows the relationship between Zeros and Coefficients of a Polynomial.
Relationship between Zeroes and Coefficients of a Polynomial
Polynomials are algebraic expressions with constants and variables that can be linear i.e. the highest power o the variable is one, quadratic and others. The zeros of the polynomials are the values of the variable (say x) that on substituting in the polynomial give the answer as zero.
While the coefficients of a polynomial are the constants that are multiplied by the variables of the polynomial. There is a relation between the Zeroes of a Polynomial and the Coefficients of a Polynomial which is widely used in solving problems in algebra.
In this article, we will learn about the Zeroes of a Polynomial, the Coefficients of a Polynomial, and their relation in detail.
Table of Content
- Zeroes of a Polynomial
- Coefficients of a Polynomial
- Relationship between Zeros and Coefficients of a Polynomial
- Linear Polynomial
- Quadratic Polynomial
- Cubic Polynomial
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