Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    11
    ReputationRep:
    I'm just having a scroll through the June 2015 AQA Further Maths paper, and this one question has got me stumped:

    In the expansion of (x+2)(x^2+kx-3) the coefficient of x^2 is 0.

    a) work out the value of k
    b) work out the coefficient of x

    On a solutions paper, the answers are a) k=-2 and b) -7; I'm not sure how this was worked out, due to the method being completely different to what I would use when expanding.

    Could someone provide a small detailed explanation of how these results were obtained?

    Thanks.
    Online

    21
    ReputationRep:
    Did you multiply out the brackets?
    Online

    21
    ReputationRep:
    You should get:
    x^3 + kx^2 -3x + 2x^2 + 2kx - 6

    When it says that the coefficient of x^2 is 0, it basically means the number in front of the x^2.
    In the expression, you have kx^2 and 2x^2, and so k + 2 = 0. Therefore, k = -2
    To get the coefficient of x, use the value of k that you just found. You have two values in the expression: -3x and 2kx
    Since you know that k is -2, you can substitute thid in to get: -3x + (2*-2)x which simplifies to -7x.
    So the coefficient of x is 7
    Hope this helped! xx

    EDIT: theholychilli
    Online

    21
    ReputationRep:
    Also, to expand the brackets, multiply everything in the second set of brackets by x, and then everything in the second set of brackets by 2
    • Thread Starter
    Offline

    11
    ReputationRep:
    (Original post by surina16)
    You should get:
    x^3 + kx^2 -3x + 2x^2 + 2kx - 6

    When it says that the coefficient of x^2 is 0, it basically means the number in front of the x^2.
    In the expression, you have kx^2 and 2x^2, and so k + 2 = 0. Therefore, k = -2
    To get the coefficient of x, use the value of k that you just found. You have two values in the expression: -3x and 2kx
    Since you know that k is -2, you can substitute thid in to get: -3x + (2*-2)x which simplifies to -7x.
    So the coefficient of x is 7
    Hope this helped! xx

    EDIT: theholychilli
    Much appreciated! Thanks, I was thinking that it would be (0x^2+kx-3) in the bracket and it didn't occur to me that it is after you have expanded it. Thanks!
    Online

    21
    ReputationRep:
    (Original post by theholychilli)
    Much appreciated! Thanks, I was thinking that it would be (0x^2+kx-3) in the bracket and it didn't occur to me that it is after you have expanded it. Thanks!
    No problem!
 
 
 
  • 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
    Have you ever participated in a Secret Santa?
    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.