Practice Solving The Equations (21.2.3) - Roots of a Polynomial - Discrete Mathematics

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6 sample questions

Question 1.
What is a root of a polynomial?
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Think of the definition we started with.
Question 2.
What is the factor theorem?
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Recall how roots relate to factors.
3Question 3.
What does the factor theorem state?
- If f(α) = 0
- then (x - α) is a factor of f(x).
- Every polynomial has exactly n factors.
- The degree of a polynomial does not affect the number of roots.
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Think about how roots relate to the factors of polynomials.
4Question 4.
True or False: A polynomial of degree n can have n distinct roots.
- True
- False
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Recall the relationship between degree and roots.
Question 5.
Given the polynomial p(x) = 2x^3 - 4x^2 + 2x, find its roots and determine its irreducible components.
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Consider using factoring techniques or the quadratic formula.
Question 6.
Factor the polynomial q(x) = x^4 + x² + 1 over complex numbers.
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Look for patterns or potential quadratic factors.

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