Hey there! Sign in to join this conversationNew here? Join for free

Further maths question help- sum of roots and argand diagrams Watch

    • Thread Starter
    Offline

    4
    ReputationRep:
    Could someone explain what they did in the mark scheme for these two questions

    Question 6c

    https://snag.gy/BKMw7d.jpg

    https://snag.gy/A7aI6Z.jpg



    Question 6c

    https://snag.gy/VK6bZ3.jpg

    https://snag.gy/84M6CR.jpg
    • Study Helper
    Offline

    13
    Study Helper
    (Original post by YAH_BOY_ASH)
    Could someone explain what they did in the mark scheme for these two questions

    Question 6c

    https://snag.gy/BKMw7d.jpg

    https://snag.gy/A7aI6Z.jpg

    If a,b,c are the roots of a cubic (f(x)), whose coeff of x^3 is 1, then

    f(x) = (x-a)(x-b)(x-c)
    = x^3-(a+b+c)x^2 + ...

    So, the sum of the roots is minus the coeff of x^2, i.e. 3 in this case.
    Hence the first line of the markscheme.

    Also, tan 9pi/12 = tan 3pi/4 = - tan pi/4 = -1
    Sub in and rearrange to get the second line.


    The maximum value of |z1-z2| will occur when z1,z2 are on the line connecting the centres of the two circles, extended. Hence the maximum distance is the distance between the two centres plus the two radii.
    • Thread Starter
    Offline

    4
    ReputationRep:
    (Original post by ghostwalker)
    If a,b,c are the roots of a cubic (f(x)), whose coeff of x^3 is 1, then

    f(x) = (x-a)(x-b)(x-c)
    = x^3-(a+b+c)x^2 + ...

    So, the sum of the roots is minus the coeff of x^2, i.e. 3 in this case.
    Hence the first line of the markscheme.

    Also, tan 9pi/12 = tan 3pi/4 = - tan pi/4 = -1
    Sub in and rearrange to get the second line.




    The maximum value of |z1-z2| will occur when z1,z2 are on the line connecting the centres of the two circles, extended. Hence the maximum distance is the distance between the two centres plus the two radii.
    Ah thank you, that makes sense, I just have a small query about the second question. I am having trouble picturing what |z1-z2| would look like in general. I understand how the length was calculated but not what |z1-z2| looks like, let me know if what i said is not clear.
    • Study Helper
    Offline

    13
    Study Helper
    (Original post by YAH_BOY_ASH)
    Ah thank you, that makes sense, I just have a small query about the second question. I am having trouble picturing what |z1-z2| would look like in general. I understand how the length was calculated but not what |z1-z2| looks like, let me know if what i said is not clear.
    |z1-z2| is the distance between z1 and z2.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Brussels sprouts
    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

    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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

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