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

Question

terenzreignz · Answer

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 · Answer

Lucky for you, it seems
$$\huge a_n = 1$$
This simplifies things...

deadshot · Answer

so, if $$a _{n}=1$$ ten how do i solve for $$a _{0}$$ ?

deadshot · Answer

*then

terenzreignz · Answer

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 · Answer

1, 3, 5, and 15, right?

terenzreignz · Answer

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 · Answer

$$\pm1, \pm3, \pm5, and \pm15$$ right?

terenzreignz · Answer

Bingo. :)

deadshot · Answer

Thanks!

terenzreignz · Answer

No problem