DeadShot
  • DeadShot
What are the possible rational zeros of f(x) = x4 + 6x3 - 3x2 + 17x - 15?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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terenzreignz
  • terenzreignz
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 \[\huge \pm \frac{p}{q}\] \[\large where \ p \ is \ a \ factor \ of \ a_0\]\[\large and \ q \ is \ a \ factor \ of \ a_n\]
terenzreignz
  • terenzreignz
Lucky for you, it seems \[\huge a_n = 1\] This simplifies things...
DeadShot
  • DeadShot
so, if \[a _{n}=1\] ten how do i solve for \[a _{0}\] ?

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DeadShot
  • DeadShot
*then
terenzreignz
  • terenzreignz
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?
DeadShot
  • DeadShot
1, 3, 5, and 15, right?
terenzreignz
  • terenzreignz
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?
DeadShot
  • DeadShot
\[\pm1, \pm3, \pm5, and \pm15\] right?
terenzreignz
  • terenzreignz
Bingo. :)
DeadShot
  • DeadShot
Thanks!
terenzreignz
  • terenzreignz
No problem

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