Practice Definition Of Roots (21.1) - Roots of a Polynomial - Discrete Mathematics

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6 sample questions

Question 1.
Define what a root of a polynomial is.
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Think about where the polynomial crosses the x-axis.
Question 2.
What is the maximum number of roots a polynomial of degree 3 can have?
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Consider the degree definition.
3Question 3.
What is a root of a polynomial?
- A value where f(x)=1
- A value where f(x)=0
- The highest degree term
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Think about where the polynomial touches the x-axis.
4Question 4.
True or False: The degree of a polynomial limits the number of roots it can have.
- True
- False
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Recall definitions surrounding polynomial properties.
Question 5.
Prove that a quadratic polynomial can have at most 2 roots.
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Consider the nature of square roots.
Question 6.
Factor the polynomial f(x) = x^3 - 3x^2 + 4x - 12 completely.
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Start with possible rational roots and use synthetic division.

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