Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Quadratics of quadratics

  1. Apr 28, 2009 #1
    Question about quadratics of quadratics

    can any 4th degree polynomial be expressed as a quadratic of a quadratic function?

    or in the more general case, can any polynomial of degree 2^n be expressed as n-many quadratic functions of quadratic functions?
    and given a polynomial of degree 2^n is there a way to find the coefficients of the quadratics?

    i tried finding a way to reduce the 4th degree poly into a quadratic of a quadratic. but the main problem is when trying to find the coefficients that i have 5 equations in 6 unknowns, so the system to find the coefficients isnt determined. why and what does this mean?



    in order for r[x] to equal p[q[x]]:


    im wondering if i could just set one of the coefficients of either quadratic equal to zero. but even then the system is unsolveable by matrices, and im not sure what terms are allowed to be zero.
  2. jcsd
  3. Apr 28, 2009 #2


    User Avatar
    Homework Helper
    Education Advisor
    Gold Member

    ????? Yes...? Are you really asking about composition of functions? If so, then, yes.
  4. Apr 28, 2009 #3


    User Avatar

    No you can't.

    If it was possible then you could always take Q0=0 and Q2=1, just by absorbing these constants into p. Then, you have 5 equations in 4 unknowns.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Quadratics quadratics Date
I Clarifying a corollary about Quadratic Forms Mar 7, 2018
B What are the applications of roots of a polynomial? Jul 1, 2017
B Roots of a quadratic equation May 18, 2017