Solve and show work for #8 6. Use the factor theorem to determine if z -1 is a factor of f(z) = 2r* + 3r - 5z +11.f(1)-211)++3(1)-s1)+7-ス3-547= S-5+7f(1)=7not oSO(x-1) is not a factor of f(x )-2x443x²Sx+77. Use the remainder theorem to find the remainder when z10 + 78 is divided by a -1 without dividing.8. . Given f(x) = x4 – 7a3 + 14x? + 2x – 20, where a = 3 + i is a root, use synthetic division to find the otherroots of f. Write f(x) in its factored form.

Name: Solve and show work for #8 6. Use the factor theorem to determine if z
Uploaded: 2024-03-20T06:46:14.000Z
Channel: Bartleby
Description: Solve and show work for #8 6. Use the factor theorem to determine if z -1 is a factor of f(z) = 2r* + 3r - 5z +11.f(1)-211)++3(1)-s1)+7-ス3-547= S-5+7f(1)=7not oSO(x-1) is not a factor of f(x )-2x443x²Sx+77. Use the remainder theorem to find the remai

Answered: 8. . Given f(x) = x* – 7x3 + 14r + 2x –…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 32E

See similar textbooks

Related questions

Concept explainers

Topic Video

Question

Solve and show work for #8

6. Use the factor theorem to determine if z -1 is a factor of f(z) = 2r* + 3r - 5z +1
1.
f(1)-211)++3(1)-s1)+7
-ス3-547
= S-5+7
f(1)=7
not o
SO
(x-1) is not a factor of f(x )-2x443x²Sx+7
7. Use the remainder theorem to find the remainder when z10 + 78 is divided by a -1 without dividing.
8. . Given f(x) = x4 – 7a3 + 14x? + 2x – 20, where a = 3 + i is a root, use synthetic division to find the other
roots of f. Write f(x) in its factored form.

Expert Solution

Step 1: Given

8) $f (x) = x^{4} - 7 x^{3} + 14 x^{2} + 2 x - 20$ , where $x = 3 + i$ .

Step 2: To determine

To find the other roots of $f$ using the synthetic division and to write $f (x)$ in the factored form.

Let, $f (x) = x^{4} - 7 x^{3} + 14 x^{2} + 2 x - 20$ .

Using the synthetic division,

$\begin{matrix} 1 \end{matrix} \begin{matrix} - 7 \\ 3 + i \end{matrix} \begin{matrix} 14 \\ - 13 - i \end{matrix} \begin{matrix} 2 \\ 4 - 2 i \end{matrix} \begin{matrix} - 20 \\ 20 \end{matrix} \begin{matrix} 1 & - 4 + i & 1 - i & 6 - 2 i & 0 \end{matrix} 3 + i$

$\Rightarrow (x - 3 - i) (x^{3} + (- 4 + i) x^{2} + (1 - i) x + (6 - 2 i))$ .

If any complex number is a root of a polynomial then it's conjugate is also a root of that polynomial.

$\Rightarrow x = 3 - i$ is also a root of the given polynomial.

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

Knowledge Booster

$Angles, Arcs, and Chords and Tangents$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage