Linear Polynomial
A linear polynomial, in general, is defined by,
y = ax + b
We know, for zeros we need to find the points at which y = 0. Solving this general equation for y = 0.
y = ax + b
⇒ 0 = ax + b
⇒ x = -b/a
This gives us the relationship between zero and the coefficient of a linear polynomial.
In general for a linear equation y = ax + b, a ≠ 0, the graph of ax + b is a straight line that cuts the x-axis at (-b/a, 0)
Example: Find the zeros of the linear polynomial.
y = 4x + 2
Solution:
Given Equation y = 4x + 2
Here,
- a = 4
- b = 2
So, by the formula mentioned above the zero will occur at (-b/a, 0) that is (-2/4, 0) or (-1/2, 0)
Let’s verify this zero using Graphical Method.
Given Equation
y = 4x + 2
In intercept Form
x/(-1/2) + y/(2) = 1
Now we know the intercepts on the x and y-axis.
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