find the complex zero of the polynomial function. Write f in factored form.

f(x)=x^4+10x^2+9

f(x)=_________________________

Question

find the complex zero of the polynomial function. Write f in factored form.

f(x)=x^4+10x^2+9

f(x)=_________________________

anonymous · Answer

it cannot be factored out

anonymous · Answer

really but it says that i should write it in a factored form. and how would you find the complex zero?

anonymous · Answer

so do I just but it in the quadratic form when i get the x^2

campbell_st · Answer

it can be factored 

$$(x^2 + 9)(x^2 + 1) = 0 $$

so the complex roots occur when 

$$x^2 + 9 = 0.....and.....x^2 + 1 = 0$$

hopefullt this helps you find them

campbell_st · Answer

so do you know how to now find the complex roots..?

anonymous · Answer

so it would be either x= -sqrt of 9 and - sqrt of 1

campbell_st · Answer

well not quite here is the start using i^2 = -1

$$x^2 = - 9 ... x = \sqrt{-9}.... x = \sqrt{9i^2}$$

campbell_st · Answer

so one pair of complex roots is 

$$x = \pm 3i$$

you just need to find the other 2 complex roots.

anonymous · Answer

oohhhhh okay but it would be +-3i and the other one would be +-1i so it would just be +-i

campbell_st · Answer

thats correct...

anonymous · Answer

so I got the answer for the complex zeros but how would it be in factored form??

campbell_st · Answer

well then you will have 4 binomials 

(x - 3i)(x+3i)... 

I'll let you get the other 2 binomials.

anonymous · Answer

okay so it would be (x-i)(x+i) and so do I but them all together like (x-3i)(x+3i)(x-i)(x+i)

campbell_st · Answer

thats correct...

anonymous · Answer

thank you for taking me through the steps!!

campbell_st · Answer

glad to help