What is the answer when the expression is factored over the complex numbers? x^2+50

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Answer 1 · 2017-11-14T16:11:22

#A=(0,50)#

roots:
#B=(5sqrt(2)*i,0)#
#C=(-5sqrt(2)*i,0)#

#(0,0) min#

#f_((x))=x^2+50#

#f_((0))=(0)^2+50=50#

#f_(x)=0#
#=> x^2+50=0#
#=> x^2=-50#
#=> x=+-sqrt(-50)#
#(sqrt(50)=sqrt(25*2)=sqrt(25)*sqrt(2)=5*sqrt(2)))#
#=> x=+-5sqrt(2)*i#

So so far so good, since we have #(0,50)# AND #(+-5sqrt(2)*i,0)#

Now we will check if we have max/min

Because #a>0# #( a*x^2+50)# the function "smiles" : )
So we have a min

#f'_((x))=2*x#

#f'_((x))=0#
#=>2*x=0#
#=>x=0#

So, we have #(0,50)# AND #(+-5sqrt(2)*i,0)# AND #(0,0) min#