1.6.1 Quadratic Equations, SPM Paper 2 (Long Questions)


Question 1:
Solve the quadratic equation, (y + 3)(y – 4) = 30

Solution:
(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
Or
y – 7 = 0
y = 7

Question 2:
Solve the quadratic equation, 5x2 = 3( x – 2) + 8

Solution:
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

Question 3:
Solve the quadratic equation
2 p 2 − 15 p = 7

Solution:
2 p 2 − 15 p = 7
2p2 – 15 = 7p
2p2 –7p – 15 = 0
(2p + 3)(p – 5) = 0
2p + 3 = 0, p =  − 3 2
Or 
p – 5 = 0
p = 5

Question 4:
Solve the quadratic equation  y ( y − 9 2 ) = 5 2

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

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