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Math Help - Is the set of degree 2 or less polynomials with p(1)=p(2) a vector space?

  1. #1
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    Angry Is the set of degree 2 or less polynomials with p(1)=p(2) a vector space?

    Use the subspace theorem to decide whether the following set is a real vector space with the usual operations. The set V of all real polynomials p of degree at most 2 satisfying p(1) = p(2), i.e. polynomials with the same values at x = 1 and x = 2.

    Subspace Thereom:
    -The set is non-empty
    - A1 is satisfied (closure under addition)
    - S1 is satisfied (closure under scalar multiplication)

    Really stuck on this!! Thanks in advance for any help
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  2. #2
    MHF Contributor
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    Re: Is the set of degree 2 or less polynomials with p(1)=p(2) a vector space?

    Hey rmcal1.

    Hint: Start off by stating what the vectors are and then show the axioms (zero vector, closure under scalar multiplication and addition).

    In other words, what does a generic vector look like when you have p(1) = p(2)?
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