pembahasan persamaan kuadrat x

7/21/2019 Pembahasan Persamaan Kuadrat x

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PEMBAHASAN SOAL PERSAMAAN KUADRAT

1. Jawab : A

x2

- 3x + 2 = 0a = 1, b = -3, c = 2

x1,2=b(b)

24.( a ) .(c)2.(a)

x1,2=(3 )(3)

24.(1 ) .(2)2.(1)

x1,2=398

2

x1,2=31

2

x1,2=31

2 x1=3+12 x1 = 2

x2=312 x2 = 1

2. Jawaban : ADiket : x2+ 2x 8 = 0 , akar akar = x1dan x2x2+ 16x 16p = 0, dengan akar akarna 2 x1dan !x2

Ditana : ni"ai p ada"a# . . . .

Jawab :

x2+ 2x 8 = 0

$ x 2 %$x +& % = 0

x1= 2 x2= -&

2 x1= &

! x2= -20

'er(a)aan ang di)ak(*d :

$x &%$ x + 20 % = 0x2+ 16x 80 = 0

16p = 80 p = !

3. Jawab :

x1+ x2= 3

x1 x2= 2

2 x1= !

x1=5

2

1


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3/10

010%2

1$8%

2

1$

2=+

++

+ xx

010%&&$%&

12$

2

=+++++

x

xx

0!18

0&01616112

2

2

=++

=++++++

xx

xxx

. Jawab :

x1,2=b(b)

24.( a ) .(c)2.(a)

x1,2=(2)(2)

2

4. (224 ) .(2)2.(2)

x1,2=2416232

4

x1,2=236162

4 =2294 2

4

x1,2=

94 24

2

=22928

4

x1,2=22(81)

2

4

x1,2=

2282

4

x1,2=24 22

4

x1=2+422

4 , adi x1 =2

x2=24 22

4 , adi x2 =44 2

4 = 1 -2

8. Jawab : 2 2x a = 0

3


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arat ra(ina" ada"a# D 4 0 dan D ada"a# bi".k*adrat (e)p*rna.

b2 &ac 4 0

$-2%2- &.1,$-a% 4 0 ....... & + &a 4 0

&$1+a% 4 0

aka $ 1 + a % )er*pakan bi".k*adrat (e)p*rna

/nt*k a = 0, 1 + 0 = 1a = 3, 1 + 3 = &

a = 8, 1 + 8 = 5

adi a = 0,3,8

5. Jawab : D

$ p + 1 %x2 2$p + 3%x + 3p = 0 )e)p*nai akar per(a)aan ke)bar )e)p*nai

(arat D = 0

Jadi b2 &ac = 0

$ 2$p + 3 %%2 & $ p+1 %.3p = 0

& $ p+ 3%2 12p$p+1% = 0

&$p2+6p+5% 12p2- 12p = 0

&p2 + 2&p + 36 12p2 - 12p = 0

-8p2+12p + 36= 0

2p2+ 3p + 5 = 0

$2p + 3%$ p -3% = 0

aka 2p + 3 = 0 ata* p -3 = 0

2p = -3 p = 3

' = -32

Jadi ni"ai p = -32 dan 3

10. Jawab : A

'er(a)aan k*adrat x

2

+ bx + c = 0 (arat )e)p*nai d*a akar ke)bar bi".k)p"ekada"a# D 7 0

Jadi b2 &ac 7 0 )aka b27 &c

11. Jawab : A

= $x-1%$x-3% = 0

= x2 &x +3 = 0

a = 1, b = -&, c = 3

rdinat titik ba"ik $b2a

,(b24ac)

4 a %

= $

1612

42.1

,% = $2,-1%

Jadi titk ba"ikna ada"a# $2,-1%

12. Jawab : D

= 8 2x x2= 0

a = -1, b = -2, c = 8

'er(a)aan (*)b* (i)etri :

x = $b2a % =

22.(1) = -1

13. Jawab :

4


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e"a"*i titik $-12 , 0%, )aka = ax2 !x 3

0 = a$-12%2 !$-12% 3

0 =1

4a+

5

23x 4

0 = a + 10 12

a = 21&. Jawab : D

2x2+ !x 3 = 0, )aka a = 2, b = !, c = -3

x1+ x2 =qb x1. x2 =

c

a

=25 =

32

1

x1+ 1

x2=x

1+x

2

x1x

2=

52

32

=5

3=12

3

1!. Jawab : 9

2x2 + 6x 1 = 0 )aka a = 2, b = 6 , c =-1

p + = =qb x1. x2 =

c

a

=62=3

=12

p2 + 2= $ p + % 2p

= $-3%2 2 $12 %

= 5 + 1

= 10

16. Jawab : 9

i(a" ' : x2 $x1 + x2% + x1x2 = 0, akar akarna x1= ; 1 dan x2 = < 1

'er(a)aan = x2+ x 2 = 0 )aka a = 1, b = , c = -2

; + < =qb = -

; < =c

a = -2

(e#ingga x1+ x2 = $; 1% + $< 1%

= ; + < 2

= --2

= -5

x1. x2 = $; 1%$< 1%

= ;< $; +


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= x2 + 5x + 6 = 0

1. Jawab = A

akar akarna 3x1 dan 3x2 dinatakan dengan 3x. n>er( 3x ada"a#x

3

?$x% = 2x2

- x ! = 0

?$x

3

= 2$x

3 2-

x

3 - ! = 0

=2x

2

9 - x ! = 0

= 2x2- 5x &! = 0

18. Jawab : 9

)x2 3x + @ = 0 , ) 0 dan a = ), b = -3, c = @

karena (a"a# (at* akarna d*a ka"i akar ang "ain, )aka x1= 2x2,(e#ingga

x1 + x2 =ab x1. x2 =

c

a

2x2 + x2 =3

m 2x2 . x2 =

1

2m

3x2 =3

m $ x2 %2 =

1

4m

x2 =1

m (

1

m)2

= 1

4m

1

m2 =

1

4m

)2= &)

)2 &) = 0

)$) - &% = 0

) = & ata* ) = 0

15. Jawab : A

&x2 px + 2! = 0 )aka a = &, b = -p, c = 2!

arat ked*a akar (a)a ada"a# D = 0

b2 &ac = 0$-p%2 &.&.2! = 0

p2 &00 = 0

$p-20%$p+20% = 0

p = 20 ata* p = -20

20. Jawab : A

2 + $) + 1% + & = 0 )aka a = 1, b = ) + 1, c = &

arat ked*a akar nata berbeda ada"a# D 4 0

b2 &ac 4 0

$)+1%2 &.1.& 4 0

2 + 2) + 1 16 4 0

2+ 2) 1! 4 0$)+!%$)-3% 4 0

6


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) 7 -! ata* ) 4 3

21. Jawab :

e"a"*i titik $-1

2 ,0%, )aka = ax2

22.23.

2&. Jawab : D

x1,2 =bD

2a

x1,2 =1414

24.5(55)25

x1,2 =14196+1100

10

x1,2 =141296

10

x1,2 =1436

10

x1 =22

10=2

1

5

x2 =5010

=5

2!. Jawab :

x1,2 =bD

2a

x1,2 =

2

929

24.2.7

x1,2 =(92)(81182+2 )56

4

x1,2 =(92)(27182 )

4

7


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x1,2 =(92)9 (322 )

4

x1,2 =(92)3(322 )

4

x1,2 =(92)3 (21)

4

x1 =(92 )+3 (21)

4=

92+3234

=11

2+1

22

x1 =(92 )3 (21 )

4=92323

4=32

26. Jawab :

x1,2 =bD

2a

x1,2 =44

24.1(3)2.1

x1,2 =428

2

x1,2 =427

2

x1=4+27

2=2+7

x2=4+27

2=27

2. Jawab : 9

x1,2 =bD

2a

x1,2 =(12)(12)

24.4 (9)

2.(4)

x1,2 =12144144

8

8


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x1,2 =120

8

x1 =12+0

8=1

1

2

x1 =120

8=1

1

2

28. Jawab : D

x1,2 =bD

2a

x1,2 =44

24.1(5)2.1

x1,2 =41620

2

x1,2 =44

2

x1,2 =42 i

2

x1 =4+2 i

2=2+i

x2 =42i

2=2i

25. Jawab =

2x2 x 3 = 0

$2x 3%$x + 1% = 0

x1= ; =3

2 ata* x2 = < = -1

& ; =4.

3

2 = 6

& < = &.$-1% = -&

'er(a)aan k*adrat ang akar akarna & ; = 6 dan & < = -& ada"a# :

$ x 6 %$ x + & % = 0

x2 2x 2& = 0

30. Jawab : 9

x2+ bx + c = 0, akar akarna x1 dan x2per(a)aan k*adrat ang akar akarna x1 + x2 dan x1.x2 ada"a# :

$x $x1 + x2 %%$ x $x1 . x2 % = 0

x1 + x2 = -b

$x $-b%%$ x c% = 0$x + b%$x c% = 0

9


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x2+ $ b c %x bc = 0

10

pembahasan persamaan kuadrat x

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