Practice Roots Of A Polynomial (23.1) - Roots of a Polynomial - Discrete Mathematics

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6 sample questions

Question 1.
What is the definition of a root of a polynomial?
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Think about what happens to the polynomial when you substitute this value.
Question 2.
How many roots can a polynomial of degree 3 have?
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Consider the maximum number of linear factors it can have.
3Question 3.
What defines a root of a polynomial?
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Think about the output of the polynomial when you substitute the value.
4Question 4.
True or False: A polynomial of degree n can have more than n roots.
- True
- False
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Remember the relationship between degree and roots.
Question 5.
Prove that a quadratic polynomial f(x) = ax^2 + bx + c can have zero, one, or two roots based on its discriminant.
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Analyze the discriminant carefully!
Question 6.
Given f(x) = x^4 + 1, demonstrate its factorization into irreducible quadratics over the field of real numbers and integers.
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Keep track of coefficients as you set up your equations!

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