Polynomial equation
from class:
Algebra and Trigonometry
Definition
A polynomial equation is an algebraic expression set equal to zero, consisting of variables with non-negative integer exponents and coefficients. It takes the form $a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0 = 0$.
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5 Must Know Facts For Your Next Test
- The degree of a polynomial equation is determined by the highest power of the variable in the equation.
- Polynomial equations can have multiple roots, which are solutions where the equation equals zero.
- The Fundamental Theorem of Algebra states that every non-zero polynomial equation has at least one complex root.
- Factoring is a common method used to solve polynomial equations, particularly those of lower degrees.
- The Rational Root Theorem helps identify possible rational solutions for polynomial equations with integer coefficients.
Review Questions
- What determines the degree of a polynomial equation?
- How can you find the roots of a quadratic polynomial equation?
- What theorem guarantees that every non-zero polynomial equation has at least one complex root?
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