Question

Resolva as equaçoes abaixo:com calculo
$5x^{2}-3x-2=0$
$x^{2} -6x=0$
$3 x^{2} +55=0$
$x^{2} -10x+25=0$
$x^{2} -x-20=0$
$x^{2} -3x-4=0$
$x^{2} -8x+7=0$

Answer 1

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}