Podcast
Play an AI-generated podcast conversation about this lesson
Download our mobile app to listen on the go
Get App
Questions and Answers
Find all the zeros of the equation $x^5 -3x^4 -15x^3 +45x^2 -16x + 48 = 0$
Find all the zeros of the equation $x^5 -3x^4 -15x^3 +45x^2 -16x + 48 = 0$
3, 4, -4, i, -i
Find all the zeros of the equation $x^3 -x^2 +5x - 5 = 0$
Find all the zeros of the equation $x^3 -x^2 +5x - 5 = 0$
i(sqrt(5)), -i(sqrt(5)), 1
Find all the zeros of the equation $7x^2 - 144 = -x^4$
Find all the zeros of the equation $7x^2 - 144 = -x^4$
3, -3, 4i, -4i
Flashcards are hidden until you start studying
Study Notes
Fundamental Theorem of Algebra
- States that every non-constant polynomial equation has at least one complex root.
- The number of roots (including multiplicity) equals the degree of the polynomial.
Key Polynomials and Their Zeros
-
Polynomial: ( x^5 - 3x^4 - 15x^3 + 45x^2 - 16x + 48 = 0 )
- Zeros: 3, 4, -4, ( i ), -( i )
-
Polynomial: ( x^3 - x^2 + 5x - 5 = 0 )
- Zeros: ( i \sqrt{5} ), -( i \sqrt{5} ), 1
-
Polynomial: ( 7x^2 - 144 = -x^4 )
- Zeros: 3, -3, 4i, -4i
Important Concepts
- Zeros can be real or complex (including imaginary units).
- The roots can be found through factoring, synthetic division, or using the quadratic formula for lower-degree polynomials.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
