# How do you use the rational roots theorem to find all possible zeros of #x^4-9x^2+20#?

##### 1 Answer

Zeros:

#### Explanation:

Given *rational* zeros must be expressible in the form

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

#+-1, +-2, +-4, +-5, +-10, +-20#

Evaluating

#f(2) = f(-2) = 16-36+20 = 0#

You can then divide

Alternatively:

Note that

#x^4-9x^2+20 = (x^2)^2-9(x^2)+20#

Note also that

So we find:

#x^4-9x^2+20#

#=(x^2-4)(x^2-5)#

#=(x^2-2^2)(x^2-(sqrt(5))^2)#

#=(x-2)(x+2)(x-sqrt(5))(x+sqrt(5))#

Hence zeros:

#x = +-2# and#x = +-sqrt(5)#