Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. problem 1. we are going to multiply the two polyno

Problem 1. We are going to multiply the two polynomials A(x) = 5 − 3x and...

70.2K

Verified Solution

Question

Advance Math

Problem 1. We are going to multiply the two polynomials A(x) = 5− 3x and B(x) = 4 + 2x to produce C(x) = a + bx + cx2 in threedifferent ways. Do this by hand, and show your work.

(a) Multiply A(x) × B(x) algebraically.

(b) (i) Evaluate A and B at the three (real) roots of unity 1,i, −1. (Note that we could use any three values.)

(ii) Multiply the values at the three roots of unity to form thevalues of C(x) at the three roots.

(iii) Plug 1, i, −1 into C(x) = a + bx + cx2 to form threesimultaneous equations with three unknowns.

(iv) Solve for a, b, c.

(c) (i) Evaluate A(x) and B(x) at the four (real) 4th roots ofunity 1, i, −1, −i.

(ii) Multiply the values at the four 4th roots to form thevalues of C(x) at the four 4th roots.

(iii) Create the polynomial D(x) = C(1) + C(i)x + C(−1)x 2 +C(−i)x 3 .

(iv) Evaluate D(x) at the four 4th roots of unity 1, i, −1, −i.(v) Use these values to construct C(x).

Answer & Explanation Solved by verified expert
3.8 Ratings (482 Votes)
    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Zin AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Q

What is the study of motivation and how does it relate to the workplace? Select any...

Operations Management
Q

What is the meaning of two conditions of EUROCODE 2 which have to be checked in...

Civil Engineering
Q

Find a system of recurrence relations for the number of n-digit quaternary sequences that contain...

Advance Math
Q

wo hikers are 13 miles apart and walking toward each other. They meet in 2...

Basic Math
Q

The price-demand equation for a particular flashlight is given by p= 113 0.004x, where x...

Basic Math
Q

A 3D printer exclusively for producing dental molar crowns, complete with all the contouring and...

Accounting
Q

Youve just been hired as an accountant at Murdstone, Inc., a retailer of supplies for...

Accounting
Q

Manufacturing overhead is usually what type of cost? O A. Step O B. Fixed O...

Accounting
Q

y m Take Test: Chapter 6 objectiv b) hbackboard.com/webapps/assessment/takelaunch.jsp?course-assessment_id-J00009-1&course-id=32250_T 58.6% QUESTION 17 A company...

Accounting
Q

Selecciona la mejor respuesta para completar la oracin: Amenazas a la independencia _________. 1....

Accounting
Q

Concord Inc. had beginning inventory of $10,800 at cost and $18,000 at retailNet purchases were...

Accounting
Q

Consider the following cash flow stream. What is the correct way to find the present...

Finance