Relation between Zeros and Coefficient
The relation between the zeros and the coefficient of the quadratic and cubic equation is discussed below.
Relation between Zeros and Coefficient for Quadratic Equation
For a quadratic equation of the form ax2 + bx + c = 0, if the two zeros of the quadratic equation are α and β, then
- Sum of root = α + β = -b/a
- Product of roots = α × β = c/a
Relation between Zeros and Coefficient for Cubic Equation
If α, β, and γ are the root of the cubic polynomial ax3 + bx2 + cx + d = 0, then the relation between its zeros and coefficients is given as follows:
- α + β + γ = -b/a
- α × β × γ= -d/a
- αβ + αγ + βγ = c/a
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
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