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H(x)=(x^2)+1 and K(x)=-(x^2)+4. If K(H)=0, what are the roots/solutions?

Guest May 24, 2017
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K(H)  =  - ( x^2 + 1)^2 + 4  ....so

 

-(x^2 + 1)^2  + 4  = 0      

 

-(x^2 + 1)^2   = -4   multiply through by -1

 

(x^2 + 1)^2   = 4     take the pos/neg square roots

 

x^2 + 1  =  ± 2

 

So...either

 

x^2 + 1  = 2          subtract 1 from both sides

 

x^2  = 1         take both square roots

 

x = ± 1

 

Or

 

x^2 + 1  = -2    subtract 1 from both sides

 

x^2  =   -3    take both square roots

 

x = ± (√3) i

 

And those are the 4 solutions

 

 

 

cool cool cool

CPhill  May 24, 2017
edited by CPhill  May 24, 2017

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