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DeadShot

  • 2 years ago

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

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  1. terenzreignz
    • 2 years ago
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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 \[\huge \pm \frac{p}{q}\] \[\large where \ p \ is \ a \ factor \ of \ a_0\]\[\large and \ q \ is \ a \ factor \ of \ a_n\]

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

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

  4. DeadShot
    • 2 years ago
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    *then

  5. terenzreignz
    • 2 years ago
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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?

  6. DeadShot
    • 2 years ago
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    1, 3, 5, and 15, right?

  7. terenzreignz
    • 2 years ago
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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?

  8. DeadShot
    • 2 years ago
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    \[\pm1, \pm3, \pm5, and \pm15\] right?

  9. terenzreignz
    • 2 years ago
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    Bingo. :)

  10. DeadShot
    • 2 years ago
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    Thanks!

  11. terenzreignz
    • 2 years ago
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    No problem

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