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Polynomial intersection question

  1. Mar 6, 2009 #1
    V1={cx^3+ax^2|c,a exists in R}
    V2={dx^3-bx^2 -d|d,b exists in R}
    find all the values of a,b that [tex]f(x)\epsilon V1\cap V2[/tex]
    ??

    find all the values of a,b that [tex]f(x)\epsilon V1+ V2[/tex]
    ??
    i know how to solve such question using vectors
    but
    they are not using using vector but some hoe check the coefficients

    ??l
     
  2. jcsd
  3. Mar 6, 2009 #2

    Mark44

    Staff: Mentor

    Can you list a specific function (with numbers instead of c and a) that belongs to V1? Can you list a specific function (with numbers instead of d and b) that belongs to V2?

    What does it take for a function to belong to both V1 and V2; i.e., to [itex]V1 \cap V2[/itex]?
     
  4. Mar 6, 2009 #3
    V1 and V2 are subspaces of [tex]R_4[x][/tex]
    polynomial field over R of power smaller then 4

    f(x)=ax^3 +bx^2 +ax -b which belongs to [tex]R_4[x][/tex]

    that all i am given
    no numbes
     
  5. Mar 7, 2009 #4

    Mark44

    Staff: Mentor

    I know what you're given. Can you use the information that you are given, and give me a specific function (with numbers instead of c and a) that belongs to V1? Can you list a specific function (with numbers instead of d and b) that belongs to V2?

    What does it take for a function to belong to both V1 and V2; i.e., to [itex]V1 \cap V2[/itex]
    ?
     
  6. Mar 8, 2009 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Was that exactly what the problem says? It looks to me like you will need a specific choice for d and c rather than a, b. For example if c= d= 0, then your functions reduce to ax^2 and -bx^2.

     
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