Relationship Between Zeroes and Coefficients of Polynomials
What does the Degree of a Polynomial mean?
The degree of the polynomial is the highest power of the independent variable it tells us how many time the curve cuts the x-axis as linear polynomial in x cut the x-axis once, whereas the quadratic polynomial in x cut the x-axis twice, etc.
What is the Relationship Between Coefficient of Polynomials and Roots of Polynomials?
Their is a definite relationship between coefficient of polynomials and roots of polynomials for a quadratic polynomial ax2 + bx + c = 0 if the zeroes of the polynomial are p, and q then,
- Sum of the roots (p+q) = -b/a
- Product of the roots(pq) = c/a
What Is the Relationship Between Zeroes and Coefficients of a Cubic Polynomial?
For the cubic polynomial, ax3 + bx2 + cx + d =0. The relationship between zeroes and coefficients of a cubic polynomial is,
- Sum of Zeroes = – Coefficient of x2/ coefficient of x3 = = -b/a
- Sum of product of Zeroes = – Coefficient of x/Coefficient of x3 = c/a
- Product of Zeroes = – Constant term/Coefficient of x3 = -d/a
What is the Relationship Between Zeroes and Coefficients of a Linear Polynomial?
For the linear polynomial ax + b = 0. The relationship between zeroes and coefficients of a linear polynomial is,
Zero of Linear Polynomial = (-b/a) = (– Constant Term/Coefficient of x)
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