## DeadShot 2 years ago What are the possible rational zeros of f(x) = x4 + 6x3 - 3x2 + 17x - 15?

1. 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$

2. terenzreignz

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

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

*then

5. 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?

1, 3, 5, and 15, right?

7. 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?

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

9. terenzreignz

Bingo. :)

Thanks!

11. terenzreignz

No problem