Practice Proof Of Roots Upper Bound (21.2.1) - Roots of a Polynomial - Discrete Mathematics

Practise this section

9 questions

Flashcard drill
4 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Define a root of a polynomial.
Show hintHide hint
Think about the equation f(x) = 0.
Question 2.
What does it mean if a polynomial is monic?
Show hintHide hint
Consider the highest degree term.
3Question 3.
What is the maximum number of roots a polynomial of degree n can have?
- n-1
- n
- n+1
Show hintHide hint
Remember the definition of polynomial degree.
4Question 4.
The factor theorem states that if f(α) = 0, then...
- True
- False
Show hintHide hint
Think about how roots relate to factors.
Question 5.
Demonstrate that if f(x) = x^n, where n is a positive integer, can yield n roots, and identify these roots.
Show hintHide hint
Consider how many times you hit zero from the polynomial.
Question 6.
Given the polynomial p(x) = x^3 - 6x^2 + 9x, factor it completely.
Show hintHide hint
Look for patterns in coefficients that connect to roots.

5 more questions in this section. Enroll free to practise them all.