5x² -3x -2 =0
a= 5 b= -3 c= -2
▲= b² -4.a.c = (-3)² -4.(5).(-2) = +9 + 40= 49
x= (-b ± √▲)/2.a
x= [-(-3) ± √49]/2.5
x= [+3 ± 7]/10
x'=[3+7]/10 = 10/10 =1
x"=[3-7]/10 = -4/10 dividindo -4 e 10 por 2 = -2/5
S= {1 ; -2/5}
x² -6x=0
x(x-6)=0
x=0
(x-6)=0
x-6=0
x= +6
S= {0 ; 6}
x² +55=0
a= 1 b= 0 c= +55
▲= b² -4.a.c = (0)² -4.1.(+55) = 0 -220= -220
▲= delta negativo, não tem raiz real.
x² -10x +25=0
a= 1 b= -10 c= +25
▲= b² -4.a.c = (-10)² -4.(1).(+25)= +100 -100=0
x= (-b ± √▲)/2.a
x=[-(-10) ± √0)/2.1
x=[+10 ± 0]/2
x'=[10+0]/2= 10/2 = 5
x"=[10-0]/2 = 10/2= 5
S= {5}
x² -x -20=0
a= 1 b= -1 c= -20
▲= b² -4.a.c = (-1)² -4.(1) .(-20)= 1+80= 81
x= (-b ± √▲)/2.a
x=[-(-1) ± √81]/2.1
x=[+1 ± 9]/2
x'=[1+9]/2= 10/2= 5
x"=[1-9]/2= -8/2 = -4
S= {5 ; -4}
x² -3x -4=0
a= 1 b= -3 c= -4
▲= b² -4.a.c = (-3)² -4.(1).(-4) = 9 +16 = 25
x= (-b ± √▲)/2.a
x=[-(-3) ± √25]/2.1
x=[+3 ± 5]/2
x'=[3 + 5]/2 = 8/2 = 4
x"=[3 -5]/2 = -2/2 = -1
S= {4 ; -1}
x² -8x +7 =0
a=1 b= -8 c= +7
▲= b² -4.a.c = (-8)² -4.(1).(+7) = 64 - 28= 36
x= (-b ± √▲)/2.a
x=[-(-8) ± √36]/2.1
x=[+8 ± 6]/2
x'=[8 +6]/2= 14/2= 7
x"=[8 -6]/2 = 2/2 = 1
S= {7 ; 1}
