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A-level Further - roots of polynomials related to existing polynomials

Discussion in 'Mathematics' started by AshgarMary, Aug 19, 2019.

  1. AshgarMary

    AshgarMary New commenter

    I'm struggling to find a real life practical reason for why one would want to use the roots of an existing polynomial as the basis for constructing another polynomial.

    Eg if roots of existing cubic are a,b,c say, find a polynomial with roots 2a+1, 2b+1, 2c+1.

    Great as an intellectual exercise but of what use in the real world (by which I don't mean postgraduate theoretical pure maths!)

    The best thing I can come up with is some kind of handwaving mutterings about 'cryptography' which to be honest I have no idea if that is true or not!

    Anyone got a real reason?
  2. Skillsheets

    Skillsheets Occasional commenter

    You are finding the equation of a transformed graph perhaps but the new spec does not mention this.
  3. AshgarMary

    AshgarMary New commenter

    Yes I get that. I like to try and give students some real life practical application - just a sentence here and there - as to why we might be doing something but am at a bit of a loss with this one!
  4. gainly

    gainly Star commenter

    I was talking about this kind of thing with a friend of mine recently. He said his reply was "That's why I don't like real life."
    Piranha likes this.
  5. maths_mikey

    maths_mikey New commenter

    Why does everything have to be useful in real life. And who knows what is going to be useful when? Lots of mathematics that is priceless to us now was useless when the methods were first being discovered. Mathematics is worthy of study in it's oen right. Stop trying to justify your subject. It should not be necessary especially to A level students.
    littlestrebel and BG54 like this.
  6. chris1729

    chris1729 New commenter

    Good question. I'm going to ponder it.i wonder if the answer might lie in situations in which an entire space is transformed, perhaps in a non-linear way.
  7. gnulinux

    gnulinux Occasional commenter

    Nothing to do with cryptography.

    The question is mildly interesting but not well posed in a number of respects. Try changing 'polynomial' to 'cubic' for a start.

    Moving the roots in the way described corresponds to stretching the graph to the right/left and up/down as if it was printed on a thin sheet of rubber.

    Now, what is made from a thin sheet of rubber that can be stretched???
  8. afterdark

    afterdark Lead commenter

    I have never had to read the script of shakespeare play but that doesn't stop English teachers teaching that and snotty kids who ask what is the real life application of something, in my experience, 9/10 are just trying to avoid doing that something.

    They are doing it because it is on the exam is a good enough reason to learn it.
    It not the teacher's role to justify everything that the government and the exam boards dictate to the teaching profession.
    Weak and **** SLT will try and argue otherwise.
    Piranha likes this.

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