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:
$\frac{-6y-2}{y}=\frac{7}{1-y}$
Solution:

Question 7:
Solve the equation:
$\frac{4m}{7}=m\left(8m-9\right)$
Solution:

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