Questão 3: Resolva as equações do 2°grau e determine suas raízes.
A)5x-3x-2=0
B)X-8x+12=0
C)X+2x-8=0
D)-X+X+12=0
E)-X+6x-5
F)6x+x-1=0
G)3x-7x+2=0
H)X=X+12
I)2x=15-X
J)X-5x+6=0
K)X-7x+12=0
L)X+3x-28=0
M)X-3=4x+2
N)(X+3)=1
O)X+9x+8=0
Me ajudem é só até amanhã!!!
Respostas
Explicação passo-a-passo:
RESOLUÇÃO!!!
5x²-3x-2=0
A=5
B=-3
C=-2
∆=b²-4ac
∆=(-3)²-4*5*-2
∆=9+40
∆=49
-b±√∆/2a
3±√49/2*5
3±7/10
X¹=3+7/10=10/10=>1
X²=3-7/10=-4/10=-4/10(÷2)=>-2/5
_____________________________
X²-8x+12=0
A=1
B=-8
C=12
∆=b²-4ac
∆=(-8)²-4*1*12
∆=64-48
∆=16
-b±√∆/2a
8±√16/2*1
8±4/2
X¹=8+4/2=12/2=>6
X²=8-4/2=4/2=>2
_____________________________
X²+2x-8=0
A=1
B=2
C=-8
∆=b²-4ac
∆=2²-4*1*-8
∆=4+32
∆=36
-b±√∆/2a
-2±√36/2*1
-2±6/2
X¹=-2+6/2=4/2=>2
X²=-2-6/2=-8/2=>-4
_____________________________
-x²+x+12=0
A=-1
B=1
C=12
∆=b²-4ac
∆=(-1)²-4*1*12
∆=1-48
∆=-47
-b±√∆/2a
-1±√-47/2*-1
-1±√-47/-2
Não possui solução no campo dos números reais.
_____________________________
-x²+6x-5=0
A=-1
B=6
C=-5
∆=b²-4ac
∆=6²-4*-1*-5
∆=36-20
∆=16
-b±√∆/2a
-6±√16/2*-1
-6±4/-2
X¹=-6+4/-2=-2/-2=>1
X²=-6-4/-2=-10/-2=>5
_____________________________
6x²+x-1=0
A=6
B=1
C=-1
∆=b²-4ac
∆=1²-4*6*-1
∆=1+24
∆=25
-b±√∆/2a
-1±√25/2*6
-1±5/12
X¹=-1+5/12=4/12=4/12(÷2)=>2/6=2/6(÷2)=>1/3
X²=-1-5/12=-6/12=-6/12(÷2)=-3/6=-3/6(÷3)=>-1/2
_____________________________
3x²-7x+2=0
A=3
B=-7
C=2
∆=b²-4ac
∆=(-7)²-4*3*2
∆=49-24
∆=25
7±√25/2*3
7±5/6
X¹=7+5/6=12/6=>2
X²=7-5/6=2/6=2/6(÷2)=>1/3
_____________________________
X²=x+12
X²-x-12=0
A=1
B=-1
C=-12
∆=b²-4ac
∆=(-1)²-4*1*-12
∆=1+48
∆=49
-b±√∆/2a
1±√49/2*1
1±7/2
X¹=1+7/2=8/2=>4
X²=1-7/2=-6/2=>-3
_____________________________
2x=15-x²
X²+2x-15=0
A=1
B=2
C=-15
∆=b²-4ac
∆=2²-4*1*-15
∆=4+60
∆=64
-b±√∆/2a
-2±√64/2*1
-2±8/2
X¹=-2+8/2=6/2=>3
X²=-2-8/2=-10/2=>-5
_____________________________
X²-5x+6=0
A=1
B=-5
C=6
∆=b²-4ac
∆=(-5)²-4*1*6
∆=25-24
∆=1
-b±√∆/2a
5±√1/2*1
5±1/2
X¹=5+1/2=6/2=>3
X²=5-1/2=4/2=>2
_____________________________
X²-7x+12=0
A=1
B=-7
C=12
∆=b²-4ac
∆=(-7)²-4*1*12
∆=49-48
∆=1
-b±√∆/2a
7±√1/2*1
7±1/2
X¹=7+1/2=8/2=>4
X²=7-1/2=6/2=>3
_____________________________
X²+3x-28=0
A=1
B=3
C=-28
∆=b²-4ac
∆=3²-4*1*-28
∆=9+112
∆=121
-b±√∆/2a
-3±√121/2*1
-3±11/2
X¹=-3+11/2=8/2=>4
X²=-3-11/2=-14/2=>-7
_____________________________
X²-3=4x+2
X²-4x-3-2=0
X²-4x-5=0
A=1
B=-4
C=-5
∆=b²-4ac
∆=(-4)²-4*1*-5
∆=16+20
∆=36
-b±√∆/2a
4±√36/2*1
4±6/2
X¹=4+6/2=10/2=>5
X²=4-6/2=-2/2=>-1
_____________________________
(X+3)²=1
X²+2x*3+3²=1
X²+6x+9=1
X²+6x+9-1=0
X²+6x+8=0
A=1
B=6
C=8
∆=b²-4ac
∆=6²-4*1*8
∆=36-32
∆=4
-b±√∆/2a
-6±√4/2*1
-6±2/2
X¹=-6+2/2=-4/2=>-2
X²=-6-2/2=-8/2=>-4
_____________________________
X²+9x+8=0
A=1
B=9
C=8
∆=b²-4ac
∆=9²-4*1*8
∆=81-32
∆=49
-b±√∆/2a
-9±√49/2*1
-9±7/2
X¹=-9+7/2=-2/2=>-1
X²=-9-7/2=-16/2=>-8
Espero ter ajudado!
