21.2.1 - Proof of Roots Upper Bound
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Practice Questions
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Define a root of a polynomial.
💡 Hint: Think about the equation f(x) = 0.
What does it mean if a polynomial is monic?
💡 Hint: Consider the highest degree term.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the maximum number of roots a polynomial of degree n can have?
💡 Hint: Remember the definition of polynomial degree.
The factor theorem states that if f(α) = 0, then...
💡 Hint: Think about how roots relate to factors.
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Challenge Problems
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Demonstrate that if f(x) = x^n, where n is a positive integer, can yield n roots, and identify these roots.
💡 Hint: Consider how many times you hit zero from the polynomial.
Given the polynomial p(x) = x^3 - 6x^2 + 9x, factor it completely.
💡 Hint: Look for patterns in coefficients that connect to roots.
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