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Bab 2 Ungkapan dan Persamaan Kuadratik

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SPM Praktis (Soalan Panjang)

Soalan 1:
Selesaikan persamaan kuadratik, (y + 3)(y – 4) = 30

Penyelesaian:
(y + 3)(y – 4) = 30
y2 – 4y + 3y – 12 = 30
y2 – y – 12 – 30 = 0
y2 – y – 42 = 0
(y + 6)(y – 7) = 0
y+ 6 = 0, y = –6
y– 7 = 0
y = 7


Soalan 2:
Selesaikan persamaan kuadratik, 5x2 = 3( x – 2) + 8

Penyelesaian:
5x2= 3( x – 2) + 8
5x2= 3x – 6 + 8
5x2– 3x – 2 = 0
(5x + 2)(x – 1) = 0
5x + 2 = 0, x = − 2 5
Or
x– 1 = 0
x= 1


Soalan 3:
Selesaikan persamaan kuadratik, 2 p 2 −15 p =7

Penyelesaian:
2 p 2 −15 p =7 

2p2– 15 = 7p
2p2–7p – 15 = 0
(2p + 3)(p – 5) = 0
2p + 3 = 0, p =  
p– 5 = 0
p= 5


Soalan 4:
Selesaikan persamaan kuadratik, y( y− 9 2 )= 5 2

Penyelesaian:
y( y− 9 2 )= 5 2 y 2 − 9y 2 = 5 2

(×2), 2y2– 9y = 5
2y2– 9y – 5 = 0
(2y + 1)(y – 5) = 0
2y + 1 = 0, y = ½
Or
y– 5 = 0
y = 5