math 3 polynomial roots
Flashcard
•
Mathematics
•
11th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the degree of the polynomial f(x) = 5x^4 - 8x^3 + 4x^2 - 6x + 3?
Back
The degree is 4.
2.
FLASHCARD QUESTION
Front
How many roots can a polynomial of degree n have?
Back
A polynomial of degree n can have at most n roots.
3.
FLASHCARD QUESTION
Front
What is a root of a polynomial?
Back
A root of a polynomial is a value of x for which f(x) = 0.
4.
FLASHCARD QUESTION
Front
What does it mean if a polynomial has a root with odd multiplicity?
Back
It means the graph of the polynomial crosses the x-axis at that root.
5.
FLASHCARD QUESTION
Front
What does it mean if a polynomial has a root with even multiplicity?
Back
It means the graph of the polynomial touches the x-axis at that root but does not cross it.
6.
FLASHCARD QUESTION
Front
If a polynomial has complex roots, what can be said about their nature?
Back
Complex roots occur in conjugate pairs.
7.
FLASHCARD QUESTION
Front
What is the Fundamental Theorem of Algebra?
Back
It states that every non-constant polynomial has at least one complex root.
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