Cubic Polynomial
A cubic polynomial is a polynomial of degree 3 and since it has its highest degree as 3, there exist three zeros of a cubic polynomial. Let’s suppose the zeros of the polynomials ax3 + bx2 + cx + d = 0 are p, q, and r, the relationship between the zeros and polynomials and the coefficient of the polynomial will be given as
Given Cubic Polynomials,
ax3 + bx2 + cx + d = 0
which has roots x = p, q and r
- Sum of the Zeroes (p + q+ r) = – Coefficient of x2/ coefficient of x3 = -b/a
- Sum of the product of the Zeroes (pq + qr + pr) = Coefficient of x/Coefficient of x3 = c/a
- Product of the zeroes (pqr) = – Constant Term/Coefficient of x3 = -d/a
Read More
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