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DeadShot Group Title

What are the possible rational zeros of f(x) = x4 + 6x3 - 3x2 + 17x - 15?

  • one year ago
  • one year ago

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  1. terenzreignz Group Title
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    The rational root test... Given a polynomial with integer coefficients \[\large a_nx^n + a_{n-1}x^{n-1}....+a_1x+a_0\] If this polynomial is to have a rational root (zero), then it will ALWAYS be of the form \[\huge \pm \frac{p}{q}\] \[\large where \ p \ is \ a \ factor \ of \ a_0\]\[\large and \ q \ is \ a \ factor \ of \ a_n\]

    • one year ago
  2. terenzreignz Group Title
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    Lucky for you, it seems \[\huge a_n = 1\] This simplifies things...

    • one year ago
  3. DeadShot Group Title
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    so, if \[a _{n}=1\] ten how do i solve for \[a _{0}\] ?

    • one year ago
  4. DeadShot Group Title
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    *then

    • one year ago
  5. terenzreignz Group Title
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    You don't *solve* for \[\large a_0\]it's given. It's the last term in the polynomial, the constant, 15. What are the factors of 15?

    • one year ago
  6. DeadShot Group Title
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    1, 3, 5, and 15, right?

    • one year ago
  7. terenzreignz Group Title
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    That's right. So those are the numerators if ever you're to have a rational root. But your leading coefficient is 1, so as I said, that simplifies things. What are your possible rational roots, then?

    • one year ago
  8. DeadShot Group Title
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    \[\pm1, \pm3, \pm5, and \pm15\] right?

    • one year ago
  9. terenzreignz Group Title
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    Bingo. :)

    • one year ago
  10. DeadShot Group Title
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    Thanks!

    • one year ago
  11. terenzreignz Group Title
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    No problem

    • one year ago
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