At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
Using the Factor Theorem, Andrew's error was at the application of the minus signal to the complex roots, and the polynomial of degree 3 is of f(x) = x³ - 7x² + 20x - 24.
What is the Factor Theorem?
The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
For this problem, the roots are given as follows:
- [tex]x_1 = 3[/tex].
- [tex]x_2 = 2 + 2i[/tex].
- [tex]x_3 = 2 - 2i[/tex].
Hence the polynomial is given as follows, considering leading coefficient a = 1:
[tex]f(x) = (x - 3)(x - 2 - 2i)(x - 2 + 2i)[/tex]
His error was at the application of the minus signal to the complex roots.
Then:
f(x) = (x - 3)[(x - 2)² - (2i)²]
f(x) = (x - 3)(x² - 4x + 4 + 4)
f(x) = (x - 3)(x² - 4x + 8)
f(x) = x³ - 7x² + 20x - 24.
More can be learned about the Factor Theorem at https://brainly.com/question/24380382
#SPJ1
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.
