Zeros of Polynomial
What are Zeros of a Polynomial?
Those such real values, for the value of polynomial becomes 0 i.e., if p(x) is a polynomial, and p(a) = 0, then x = a is the zero of p(x).
How to find the Zeros of a Polynomial?
There is various method for various different polynomials to find zeroes such as for quadratic spilling the middle term and quadratic formula. For linear, simple rearrangement of variables and for cubic we use a combination of rational root theorem, long division, factor theorem and remainder theorem.
Can a Polynomial have more than One Zero?
Yes, a polynomial can have more than one zero, in fact, the polynomial of n degrees can have at most n real zeros.
What is the Multiplicity of a Zero of a Polynomial?
In the factorization process, one factor or one zero of a polynomial then a number of times a factor or a zero came, that is called the multiplicity of that root.
What is the Fundamental Theorem of Algebra?
The fundamental Theorem of algebra states “If P(x) is a polynomial of degree “n” then P(x) will have exactly n zeros, some of which may repeat.”
Does a Polynomial with a Degree n always have n Real Roots?
No, a polynomial with degree n doesn’t always have n real roots, as some roots can be imaginary or complex numbers.
What is the Degree of Zero Polynomial?
The degree of zero polynomial is zero.
Zeros of Polynomial
Zeros of a Polynomial are those real, imaginary, or complex values when put in the polynomial instead of a variable, the result becomes zero (as the name suggests zero as well). Polynomials are used to model some physical phenomena happening in real life, they are very useful in describing situations mathematically.
The zeros of a polynomial are all the x-values that make the polynomial equal to zero. Zeroes of a polynomial tell us about the x-intercepts of the polynomial’s graph. In this article, we will discuss about the zeroes of a polynomial, how to find them, the factor theorem, etc.
Table of Content
- What are Zeros of Polynomials?
- Zeros of Polynomial Formula
- How to Find Zero of a Polynomial?
- For Linear Polynomial
- For Quadratic Polynomial
- For Cubic Polynomial
- Factor Theorem
- Relation between Zeros and Coefficient
- Relation between Zeros and Coefficient for Quadratic Equation
- Relation between Zeros and Coefficient for Cubic Equation
- Forming Equation with Zeros of Polynomial
- Zeros in Graph of Polynomials
- Fundamental Theorem of Linear Algebra
- Multiplicity of a Root
- Articles related to Zeros of Polynomial
- Sample Problems on Zeros of Polynomial
- Practice Problems on Zeros of Polynomial