Quadratic Equations Long Questions (Question 5 – 8)


Question 5:
Solve the equation:
(m + 2)(m – 4) = 7(m – 4).
 
Solution:
(m + 2)(m – 4) = 7(m – 4)
m2– 4m + 2m – 8 = 7m – 28
m2– 9m + 20 = 0
(m – 5)(m – 4) = 0
m= 5 or m = 4   


Question 6:
Solve the equation:
6 y 2 y = 7 1 y

Solution:

6 y 2 y = 7 1 y ( 6 y 2 ) ( 1 y ) = 7 y 6 y + 6 y 2 2 + 2 y 7 y = 0 6 y 2 11 y 2 = 0 ( 6 y + 1 ) ( y 2 ) = 0 6 y + 1 = 0 or y = 2 y = 1 6


Question 7:
Solve the equation:
4 m 7 = m ( 8 m 9 )

Solution:
4 m 7 = m ( 8 m 9 ) 4 m = 7 m ( 8 m 9 ) 4 m = 56 m 2 63 m 56 m 2 63 m 4 m = 0 56 m 2 67 m = 0 m ( 56 m 67 ) = 0 m = 0 or 56 m 67 = 0 m = 67 56


Question 8:
Diagram above shows a rectangle ABCD.
(a) Express the area of ABCD in terms of n.
(b) Given the area of ABCD is 60 cm2, find the length of AB.
 
Solution:
(a)
Area of ABCD
= (n + 7) × n
= (n2+ 7n) cm2

(b)
Given the area of ABCD = 60
n2+ 7n = 60
n2+ 7n – 60 = 0
(n – 5) (n + 12) = 0
n= 5 or    n = – 12 (not accepted)
 
When n = 5,
Length of AB= 5 + 7 = 12 cm

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