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Hi, I just have one question.

 

What is the number of complex zeros for the polynomial function f(x)=x^4+5x^2+6? 

Thats all, thanks

 Nov 9, 2017
 #1
avatar+771 
+1

Whatever the highest degree is in a polynomial is the number of complex factors.

Therefore, in this equation there are 4 real complex numbers.

 Nov 9, 2017
 #2
avatar+98005 
+1

x^4 + 5x^2 + 6  = 0

 

We  can factor this as

 

(x^2  + 3) (x^2 + 2)  = 0

 

Setting each factor to 0  we have that

 

x^2  + 3  =  0               x^2  + 2  = 0

 

x^2  =  -3                     x^2  =  -2

 

Note that no real numbers make these true, so, there are 4 complex zeroes

 

 

cool cool cool

 Nov 9, 2017

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