# How do you find all zeros of the function #f(x)= x^4 + 5x^2 + 4# given -i as a zero?

##### 1 Answer

Apr 6, 2016

#### Answer:

Factor by grouping to find:

#x = +-i# or#x = +-2i#

#### Explanation:

This polynomial factors by grouping as follows:

#f(x) = x^4+5x^2+4#

#= x^4+4x^2+x^2+4#

#= x^2(x^2+4)+1(x^2+4)#

#= (x^2+1)(x^2+4)#

#= (x^2-i^2)(x^2-(2i)^2)#

#= (x-i)(x+i)(x-2i)(x+2i)#

Hence zeros:

Another way of finding this is to note that since

So if

Therefore

Then dividing

#f(x) = (x^2+1)(x^2+4)#

Hence the other two zeros are