# How do you find all the zeros of #f(x)=x^4-8x^3+17x^2-8x+16 #?

##### 1 Answer

May 1, 2016

#### Answer:

Zeros at

#### Explanation:

Given

By the rational root theorem, we know that any rational roots must be factors of

which implies they must be in the set

Testing each of these possibilities give a zero at (an only at)

If we divide

we get factors

Again, applying the factor theorem of

we find the only zero at

Dividing

we can re-factor as