Coefficients of a Polynomial
A polynomial is a function of x and its powers. It can be linear, quadratic, and others. A coefficient of a polynomial is the numerical value related to each x and its power in the polynomial.
For example, in the linear polynomial ax + b the coefficient of x is ‘a’ similarly, in px2 + qx + r the coefficient of x2 is ‘p’ and the coefficient of x is ‘q’
The coefficient of a polynomial can be any real number, fractions, or decimals and they can also be imaginary numbers.
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