Zeroes of a Polynomial
For any polynomial f(x) zeros of the polynomial are defined as the values of the x which substituting in f(x) results in the zero value of the polynomial. They are also called the solution of the polynomial. Mathematically we define the zero of the polynomial as for any polynomial f(x) a is the zero of the polynomial if
f(a) = 0
For example, if the given polynomial is f(x) = x+3 then -3 is the zero of the polynomial as,
f(-3) = -3+3 =0
The number of zeroes of the polynomial depends on the degree of the polynomial, i.e. for a linear polynomial (polynomial with degree 1) we have 1 zero, for a quadratic polynomial (polynomial with degree 2) we have 2 zeros, and so on.
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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