k:=100
cv:=30
θ:=80
f1:=((-((k α)/(((-1+α))^2))-(θ/(2 (((-1+α))^2)))+((α θ)/(2 (((-1+α))^2)))+((2 (Sqrt[k (cv (((-1+α))^2)+k (α^2)+θ-α θ)]))/(((-1+α))^2)))/((1/(2 (((-1+α))^2)))-(α/(2 (((-1+α))^2)))))
pf1=Plot[{f1,0},{α,0,1},GridLines->{{1},{}}]

Show[pf1,AxesLabel->{HoldForm[α],None},PlotLabel->None,LabelStyle->{GrayLevel[0]}]

Show[%16,AxesLabel->{HoldForm[α],HoldForm[F]},PlotLabel->None]

pf1=Plot[{f1,0},{α,0,1},GridLines->{{1},{}},Filling->{{1->{Top,ColorData["HTML"]["Silver"]},{1->{{2},ColorData["HTML"]["Gainsboro"]}}}}]

Show[pf1,ImageSize->Large]

Show[%60,AxesLabel->{HoldForm[α],HoldForm[F]},PlotLabel->None,LabelStyle->{FontFamily->"Baskerville",GrayLevel[0]}]

Show[%61,Background->None]

Show[pf1,AxesStyle->Black]

k:=100
cv:=30
θ:=80
f1:=((-((k α)/(((-1+α))^2))-(θ/(2 (((-1+α))^2)))+((α θ)/(2 (((-1+α))^2)))+((2 (Sqrt[k (cv (((-1+α))^2)+k (α^2)+θ-α θ)]))/(((-1+α))^2)))/((1/(2 (((-1+α))^2)))-(α/(2 (((-1+α))^2)))))

kb:=60
k:=100
cv:=30
cvb:=10
θ:=80
f2:=((-((kb α)/(((-1+α))^2))-(θ/(2 (((-1+α))^2)))+((α θ)/(2 (((-1+α))^2)))+((2 (Sqrt[kb (cv (((-1+α))^2)+cvb (((-1+α))^2)+kb (α^2)+θ-α θ)]))/(((-1+α))^2)))/((1/(2 (((-1+α))^2)))-(α/(2 (((-1+α))^2)))))


pf1=Plot[{f1,f2,0},{α,0,1},GridLines->{{1},{}},Filling->{{1->{Top,ColorData["HTML"]["Silver"]},{1->{{2},ColorData["HTML"]["DarkGray"]}},
{2->{{3},ColorData["HTML"]["Gainsboro"]}}}}]

Show[pf1,AxesLabel->{HoldForm[α],None},PlotLabel->None,LabelStyle->{GrayLevel[0]}]

Show[%24,ImageSize->Large]

Show[pf1,ImageSize->Large]

if α < 0.5

f1:=((-((k α)/(((-1+α))^2))-(θ/(2 (((-1+α))^2)))+((α θ)/(2 (((-1+α))^2)))+((2 (Sqrt[k (cv (((-1+α))^2)+k (α^2)+θ-α θ)]))/(((-1+α))^2)))/((1/(2 (((-1+α))^2)))-(α/(2 (((-1+α))^2)))))
pf1=Plot[{f1,0},{α,0,0.8},GridLines->{{0.8},{}},AxesLabel->{HoldForm[α],HoldForm[F]},PlotLabel->None,LabelStyle->{GrayLevel[0]}]

Show[pf1,AxesLabel->{HoldForm[α],HoldForm[F]},PlotLabel->None,LabelStyle->{GrayLevel[0]}]

f2:=((-((kb α)/(((-1+α))^2))-(θ/(2 (((-1+α))^2)))+((α θ)/(2 (((-1+α))^2)))+((2 (Sqrt[kb (cv (((-1+α))^2)+cvb (((-1+α))^2)+kb (α^2)+θ-α θ)]))/(((-1+α))^2)))/((1/(2 (((-1+α))^2)))-(α/(2 (((-1+α))^2)))))


pf1=Plot[{f1,f2,0},{α,0,0.8},GridLines->{{0.8},{}},AxesLabel->{HoldForm[α],HoldForm[F]},PlotLabel->None,LabelStyle->{GrayLevel[0]}]

Show[pf1,AxesLabel->{HoldForm[α],HoldForm[F]},PlotLabel->None,LabelStyle->{GrayLevel[0]}]