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

    2
    ReputationRep:
    Solve the following equation
     \displaystyle x^4+6x^3+5x^2-12x-5=0 .
    Any ideas ??
    Offline

    11
    ReputationRep:
    (Original post by Ano123)
    Solve the following equation
     \displaystyle x^4+6x^3+5x^2-12x-5=0 .
    Any ideas ??
    What sort of thing is this for, the roots aren't very pleasant you're going to need to be creative or use a rather complicated and unpleasant method.
    That is, unless you're permitted to stick it into a computational engine.
    EDIT: Ignore me, I'll go back to sleep
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by joostan)
    What sort of thing is this for, the roots aren't very pleasant you're going to need to be creative or use a rather complicated and unpleasant method.
    That is, unless you're permitted to stick it into a computational engine.
    The roots are nice.
    • TSR Support Team
    • Very Important Poster
    • Welcome Squad
    Offline

    20
    ReputationRep:
    TSR Support Team
    Very Important Poster
    Welcome Squad
    (Original post by Ano123)
    Solve the following equation
     \displaystyle x^4+6x^3+5x^2-12x-5=0 .
    Any ideas ??
    (x^2+bx+c)(x^2+dx+e)=x^4+6x^3+5x  ^2-12x-5


    (Original post by joostan)
    What sort of thing is this for, the roots aren't very pleasant you're going to need to be creative or use a rather complicated and unpleasant method.
    That is, unless you're permitted to stick it into a computational engine.
    As 5 is prime, can't you infer c and e easily and compare coefficients for the rest?
    Offline

    11
    ReputationRep:
    (Original post by Kvothe the arcane)
    (x^2+bx+c)(x^2+dx+e)=x^4+6x^3+5x  ^2-12x-5




    As 5 is prime, can't you infer c and e easily and compare coefficients for the rest?
    Very good point, I have been a wee bit silly .


    (Original post by Ano123)
    The roots are nice.
    Well, I wouldn't go that far, but I guess they could be worse.
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by joostan)
    Very good point, I have been a wee bit silly .



    Well, I wouldn't go that far, but I guess they could be worse.
    As far as quartic equations go the roots are nice
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by Kvothe the arcane)
    (x^2+bx+c)(x^2+dx+e)=x^4+6x^3+5x  ^2-12x-5




    As 5 is prime, can't you infer c and e easily and compare coefficients for the rest?
    I solved it by completing the square, didn't try factorising it but you're right it factorises nicely into two quadratic factors.
    Offline

    22
    ReputationRep:
    (Original post by Kvothe the arcane)
    As 5 is prime, can't you infer c and e easily and compare coefficients for the rest?
    Not sure what you mean by this?

    Why can't you have (x^2 + bx + \sqrt{5})(x^2 + cx - \sqrt{5})?
    Offline

    21
    (Original post by Zacken)
    Not sure what you mean by this?

    Why can't you have (x^2 + bx + \sqrt{5})(x^2 + cx - \sqrt{5})?
    Well that's certainly stirred things up...
    • TSR Support Team
    • Very Important Poster
    • Welcome Squad
    Offline

    20
    ReputationRep:
    TSR Support Team
    Very Important Poster
    Welcome Squad
    (Original post by Zacken)
    Not sure what you mean by this?

    Why can't you have (x^2 + bx + \sqrt{5})(x^2 + cx - \sqrt{5})?
    For such a quartic to be solvable for an a-level student, I assumed (perhaps wrongly?) that the c coefficient of the quadratics would have to be an integer.
    Offline

    22
    ReputationRep:
    (Original post by Kvothe the arcane)
    For such a quartic to be solvable for an a-level student, I assumed (perhaps wrongly?) that the c coefficient of the quadratics would have to be an integer.
    It's not really a fair assumption - it's okay assuming something like "Oh yeah, this is an A-Level quartic so I should try and check whether the first few integers are roots" and then having that not pan out, but making that kind of a mathematical assumption isn't very valid. (imo)
    Offline

    11
    ReputationRep:
    (Original post by Zacken)
    It's not really a fair assumption - it's okay assuming something like "Oh yeah, this is an A-Level quartic so I should try and check whether the first few integers are roots" and then having that not pan out, but making that kind of a mathematical assumption isn't very valid. (imo)
    I agree, but it is a very reasonable first attempt to guess a factorisation, and happens to work out, and makes the problem far simpler than I was making it.
    • TSR Support Team
    • Very Important Poster
    • Welcome Squad
    Offline

    20
    ReputationRep:
    TSR Support Team
    Very Important Poster
    Welcome Squad
    I stand corrected :getmecoat:.

    Zacken, joostan
    • PS Reviewer
    Offline

    20
    ReputationRep:
    PS Reviewer
    (Original post by Zacken)
    It's not really a fair assumption - it's okay assuming something like "Oh yeah, this is an A-Level quartic so I should try and check whether the first few integers are roots" and then having that not pan out, but making that kind of a mathematical assumption isn't very valid. (imo)
    And whilst you make a valid point, there are better ways of saying this instead of publicly humiliating users who are genuinely helping. I'm just saying.
    Offline

    18
    ReputationRep:
    (Original post by Slowbro93)
    And whilst you make a valid point, there are better ways of saying this instead of publicly humiliating users who are genuinely helping. I'm just saying.
    He didn't really humiliate, did he? Also Kvothe and Zain are good friends (I think)
    Offline

    22
    ReputationRep:
    (Original post by Slowbro93)
    And whilst you make a valid point, there are better ways of saying this instead of publicly humiliating users who are genuinely helping. I'm just saying.
    I wasn't trying to come across as humiliating anybody - I'm sorry if that's how it came across, KTA. I rush and end up being more blunt than I'd like sometimes. I hope you know that I wouldn't say anything out of malice to you. But thanks for bringing it up Slowbro, I'll try and look over the tone of my post before posting in the future.
 
 
 
  • 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
    Would you like to hibernate through the winter months?
    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.