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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the definition of a root of a polynomial?
💡 Hint: Think about what happens to the polynomial when you substitute this value.
Question 2
Easy
How many roots can a polynomial of degree 3 have?
💡 Hint: Consider the maximum number of linear factors it can have.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What defines a root of a polynomial?
💡 Hint: Think about the output of the polynomial when you substitute the value.
Question 2
True or False: A polynomial of degree n can have more than n roots.
- True
- False
💡 Hint: Remember the relationship between degree and roots.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that a quadratic polynomial f(x) = ax^2 + bx + c can have zero, one, or two roots based on its discriminant.
💡 Hint: Analyze the discriminant carefully!
Question 2
Given f(x) = x^4 + 1, demonstrate its factorization into irreducible quadratics over the field of real numbers and integers.
💡 Hint: Keep track of coefficients as you set up your equations!
Challenge and get performance evaluation