Question

What are the posible rational zeros of f(x)= x4 +6x^3-3x^2+ 17x-15

Answer 1

`w(x)=a_nx^n+a_(n-1)x^(n-1)+a_(n-2)x^(n-2)+...+a_1x+a_0`

The posible rational zeros of w(x) are:

`\pm\text{dividers of}\ a_0\ \text{and}\ \pm\frac{\text{dividers of}\ a_0}{\text{dividers of}\ a_n}`

`f(x)=x^4+6x^3-3x^2+17x-15\to a_n=1,\ a_0=-15`

`\text{dividers of}\ a_0= 15:\ \ 1,\ 3,\ 5,\ 16\\\text{dividers\ of}\ a_n=1:\ \ 1`

Answer:

`\{\pm1,\ \pm3;\ \pm5;\ \pm15\}`