Page 87 - Mathematics_Form_Two

Algebra

previous one by 50 shillings. That is,
hence, a = − 400, b = 317,and c = − 60.
3 600 3 600 = 50 .
−
By using the quadratic formula, x x + 6
3 600(x + 6) 3 600x− = 50 (xx + 6)
2
− b − 4ac 2
b
k = 3 600x + 21 600 3 600x− = 50x + 300x
2a 21 600 50x= 2 + 300x
FOR ONLINE READING ONLY
Substitute the values of a, b, and c, Simplify the equation by dividing each
2
4( 400)( 60)
− (317)  (317) −− − term by 50:
k = 2
2( 400) x + 6x − 432 0= , implying that Mathematics for Secondary Schools
−
6
a = 1, b = ,and c = − 432. From the
− 317  100 489 96 000 quadratic formula,
−
k =
− 800 −± b − 4ac
2
b
x =
− 317 4 489 − 317 67 2a

k = =
− 800 − 800 − 6 ± 6 − 4 1 ( 432)× ×−
2
=
− − 317 67+317 67+ − − 317 67−317 67− 21×
Either, k = = or k
or k = =
Either,
or
Either, k
800
− − 800 −800 − 800 −± 36 1728+
6
55 12 12 =
Therefore, k = k = or k . . 2
or
or k ==
16 16 25 25
6
= −± 1764
Example 4�43 2
6
Juma bought a certain number of = −± 1764
mangoes for 3,600 shillings. If each 2
mango had been sold for 50 shillings = −±
6 42
less, he could have bought six more 2
mangoes for the same amount of money. −+ −−
6 42
6 42
How many mangoes did he buy? Either, x = 2 or x = 2
Solution x = 18 or x = − 24
Let x be the number of mangoes Checking: With 18 mangoes each costs
bought. The price of each mango was 200 shillings. Six more mangoes each
3 600 shillings. Six more mangoes costs 150 shillings.
x
correspond to (x + 6) mangoes. The difference is
Hence, each mango would cost (200 – 150) shillings = 50 shillings.
3 600 . shillings. Therefore, the number of mangoes

x + 6 bought was 18 because it is impossible
This price per mango is less than the to have a negative number of mangoes.

81
Student's Book Form Two

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MATHEMATIC F2 v5.indd 81