Turn on thread page Beta
    • Thread Starter
    Offline

    9
    ReputationRep:
    x^3 - 5x + 3 = 0 (I'm going to call the roots A, B, and Y as latex isn't working)

    Find A + B + Y (0)

    Find A^2 + B^2 + Y^2 (10)

    Find A^3 + B^3 + Y^3

    I tried multiplying the first and second parts of the question together to see if it simplified down to A^3 + B^3 + Y^3 + some other stuff, but I couldn't get it in terms of Sigma(A), Sigma(AB) and ABY.

    I know that Sigma(A^2) = [Sigma(A)]^2 - 2(Sigma(AB))
    Is there a similar formula for Sigma(A^3) that I am supposed to use?
    • Study Helper
    Offline

    15
    Study Helper
    (Original post by __Adam__)
    x^3 - 5x + 3 = 0 (I'm going to call the roots A, B, and Y as latex isn't working)

    Find A + B + Y (0)

    Find A^2 + B^2 + Y^2 (10)

    Find A^3 + B^3 + Y^3

    I tried multiplying the first and second parts of the question together to see if it simplified down to A^3 + B^3 + Y^3 + some other stuff, but I couldn't get it in terms of Sigma(A), Sigma(AB) and ABY.

    I know that Sigma(A^2) = [Sigma(A)]^2 - 2(Sigma(AB))
    Is there a similar formula for Sigma(A^3) that I am supposed to use?
    Whilst there is a formula, it's not necessary.

    Since A is a root of your polynomial x^3 - 5x + 3 = 0, then

    A^3 - 5A + 3=0

    Similarly for B,C.

    Add the three equations, and ....
    • Thread Starter
    Offline

    9
    ReputationRep:
    (Original post by ghostwalker)
    Whilst there is a formula, it's not necessary.

    Since A is a root of your polynomial x^3 - 5x + 3 = 0, then

    A^3 - 5A + 3=0

    Similarly for B,C.

    Add the three equations, and ....
    Never thought of trying that, thanks!
    • Study Helper
    Offline

    15
    Study Helper
    (Original post by __Adam__)
    Never thought of trying that, thanks!
    np.

    As an extension you might like to consider what the sum of the fourth powers is.

    Route to answer in the spoiler

    Spoiler:
    Show

    Multiply the original polynomial by x, and proceed as for the cubes.


    And the fifth,...

    until you're bored.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: November 17, 2013

University open days

  • University of Roehampton
    All departments Undergraduate
    Sat, 17 Nov '18
  • Edge Hill University
    Faculty of Health and Social Care Undergraduate
    Sat, 17 Nov '18
  • Bournemouth University
    Undergraduate Open Day Undergraduate
    Sat, 17 Nov '18
Poll
Black Friday: Yay or Nay?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Equations

Best calculators for A level Maths

Tips on which model to get

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.