Quadratic Equations (PPT)-SMK JUGRA

8/7/2019 Quadratic Equations (PPT)-SMK JUGRA

1/12

TOPIC: QUADRATIC EQUATIONS (SET 1)

6 (a) Express the quadratic equation2(3 2) 5 x x x = + in its general form.

Ungkapkan persamaan kuadratik2

(3 2) 5 x x x = + dalam bentuk am.

(2 marks)

(b) Given1

2and 5 are the roots of a quadratic equation. Write the quadratic

equation in the form of 2 0ax bx c+ + =

Diberi1

2dan 5 ialah dua punca persamaan kuadratik. Tulis persamaan

kuadratik dalam bentuk 2 0ax bx c+ + = . (2 marks)

7. It is given that 2 is one of the roots of the quadratic equation 28 2 0h x x = .Find the value ofh.Diberi 2 ialah satu daripada punca bagi persamaan kuadratik 28 2 0h x x = .Cari nilai h. (2 marks)

8. Given and are the roots of the quadratic equation 22 8 5 0x x+ + = .Diberi dan ialah punca persamaan kuadratik 22 8 5 0x x+ + = .

(a) Find the values of + and .Cari nilai + dan .

(b) Form the quadratic equation which has the roots 2 and 2 .Bentukkan persamaan kuadratik yang mempunyai punca 2 and 2 .

(4 marks)

9. Solve the quadratic equation (2 5) 2 1 x x x+ = + . Give the answer correct to three

decimal places.

Selesaikan persamaan kuadratik (2 5) 2 1x x x+ = + . Berikan jawapan betul kepadatiga tempat perpuluhan(3marks)


2/12

10. The quadratic equation28 3 4 4 ,px p x+ = where p is a constant, has two equal

roots. Find the values ofp .

Persamaan kuadratik2

8 3 4 4 ,px p x+ = di mana p ialah pemalar, mempunyai duapunca yang sama. Cari nilai p .

(3 marks)

11. One of the roots of the quadratic equations 24 3 0x kx + = is three times the otherroots, find the values of k.

Satu daripada punca persamaan kuadratik 24 3 0x kx + = adalah tiga kali puncayang satu lagi. Cari nilai k.

(3 marks)


3/12

SKEMA JAWAPAN SET 1

NO JAWAPAN MARKAH

6 (a) 2

3(3 2) 5x x = +

29 6 5x x = + 2 9 11 0x x + =

11

6 (b) (2 1)( 5) 0x x + =22 10 5 0x x x+ =

22 9 5 0x x+ =

1

1

7 When x=2, 28 2 0h x x =

28( 2) 2( 2) 0h =

16 8 0h + = 8h =

1

1

8 (a) 22 8 5 0x x+ + =

2 5( 4) 0

2x x + =

Thus, + = 4

=5

2

1

1

8 (b) The roots are 2 and 2

SOR = 2 + 2 . POR = (2 ) ( 2 )= 2 ( + ) = 4 .

= 2 (- 4 ) = 4 (5

2)

= - 8 = 10

The quadratic equation is2 ( 8) 10 0x x + =

2

8 10 0x x+ + =

1

1

9 (2 5) 2 1 x x x+ = +22 5 2 1 0x x x+ =

22 3 1 0x x+ =


4/12

x3 9 8

4

+=

3 9 8

4

+=

3 17

4

=

0.281= or 1.781

1

1.1

10 8 4 3 4 0 px x p+ + =

2 4 0b ac =2

4 4(8 )(3 4 ) 0p p =

216 96 128 0p p + =

(2 1)(4 1) 0x x =2 1 0x = or 4 1 0x =

1

2x =

1

4x =

1

1,1

11 24 3 0x kx + =2 3 3

04 4

x x + =

Let the roots be and 3

+ 3 =4

k (3) =

3

4

4 =4

k

2 334

=

1

2 =

When1

2 = , 4

4

k =

1

4 2 4

k

= 8k=

1

1

1


5/12

QUADRATIC EQUATIONS (SET 2)

6. Given the quadratic equation23 ( 4)x= .

Diberi persamaan kuadratik2

3 ( 4)x= .

(a) Express the given quadratic equation in the general form 2 0ax bx c+ + =Ungkapkan persamaan kuadratik yang diberi dalam bentuk am 2 0ax bx c+ + =

(2 marks)

(b) Hence, from your answer in (a) determine the types of roots.

Seterusnya, daripada jawapan di (a), tentukan jenis punca.(2 marks)

7. Form the quadratic equation which has roots 3 and 4 . Give your answer in the

form0

2=++ cbxax

, where a, b and c are constants.Bentukkan persamaan kuadratik dengan punca -3 dan 4. Beri jawapan anda dalam

bentuk 02 =++ cbxax , di mana a, b, dan c ialah pemalar.

(2 marks)

8. The quadratic equation2

2 0x px q+ + = has roots 4 and 2 . FindPersamaan kuadratik

22 0x px q+ + = mempunyai punca 4 dan 2 . Cari

(a) the values ofp and q .

nilai bagi p dan q

(b) the range of the values ofk so that22x px q k + + = has no real roots.

Cari julat nilai k jika22x px q k + + = tidak mempunyai punca nyata.

(4 marks)

9. Solve the quadratic equation h2 3h + 2 = 2(h 1).

Selesaikan persamaan kuadratikh2 3h + 2 = 2(h 1).(3 marks)


6/12

10. Given m and 2m are the positive roots of the quadratic equation2 18 0x px + = .

Find the values ofm andp.

Diberi m dan 2m ialah punca positif bagi persamaan kuadratik2 18 0x px + = .

Cari nilai m dan nilai p.

(3 marks)

11. The quadratic equation2

2 ( 2 ) 2x x p x p+ = has two distinct roots. Find the rangeof values ofp.

Persamaan kuadratik2

2 ( 2 ) 2 x x p x p+ = mempunyai dua punca yang berbeza.

Cari julat bagi nilai p.

(3 marks)


7/12

SKEMA JAWAPAN SET 2

NO JAWAPAN MARKAH

6 (a) 2( 4) 3x =

2 8 16 3x x + = 2 8 13 0x x + = 11

6 (b) 2 24 ( 8) 4(1)(13)b ac =

64 52

12

= => 0

The equation has two different roots.

1

1

7 ( 3)( 4) 0x x+ = 2 4 3 12 0x x x + =

2 12 0x x =

1

1

8(a) 22 0x px q+ + =

2 0

2 2

p qx x

+ =

From the roots -4 and 2

SOR =2

P POR =

2

q

4 2 2

p

+ = 4(2) 2q

= 4p = 16q = 1,1

8(b) 22 4 16x x k + = 22 4 16 0x x k + = 2 4b ac < 0

2(4) 4(2)( 16 )k < 0

16 + 128 + 8k < 0

8k < 144

k 0

2 2(4 1) 4(2)(2 )p p > 0

2 216 8 1 16p p p + > 0

8p > 1

p 3

1

1

1

10 23 9 5 0x x =2( 9) ( 9) 4(3)( 5)

2(3)x

=

1


12/12

9 141

6x

=

3.479, 0.4791x = 1,1

11 From2

0x mx p m + + = , SOR = m POR =p+m

Given 3 and p are the roots,

3m p= + .(1) 3p m p+ = .(2)

Substitute (1) into (2)3 3p p p+ + = when 3p = , 3 3m = +

3p = 6=

1

1,1

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Quadratic Equations (PPT)-SMK JUGRA