## College Algebra (10th Edition)

Maximum number of zeros: $4.$ 1 positive, 1 negative zero.
$(-x)^{n}=\left\{\begin{array}{ll} x^{n} & \text{if n is even}\\ -x^{n} & \text{if n is odd} \end{array}\right.$ --- $f(x)=5x^{4}+2x^{2}-6x-5$ has 1 change in signs, from $+2x^{2}$ to $-6x$. By Descartes’ Rule of Signs, f has 1 positive zero. $f(-x)=5x^{4}+2x^{2}+6x-5$ has 1 change in signs, so it has 1 negative zero. The degree of the polynomial is 4, which is the maximum number of zeros.