# What are all the possible rational zeros for #f(x)=x^4-7x^2+10# and how do you find all zeros?

##### 1 Answer

Nov 20, 2016

#### Answer:

#### Explanation:

Given:

#f(x) = x^4-7x^2+10#

By the rational root theorem, any *rational* zeros of

That means that the only possible *rational* zeros are:

#+-1, +-2, +-5, +-10#

However, note that we can factor

#x^4-7x^2+10 = (x^2-5)(x^2-2)#

#color(white)(x^4-7x^2+10) = (x^2-(sqrt(5))^2)(x^2-(sqrt(2))^2)#

#color(white)(x^4-7x^2+10) = (x-sqrt(5))(x+sqrt(5))(x-sqrt(2))(x+sqrt(2))#

So the only zeros of