Quadratic equations f4 level

2010-09-15 3:55 am
1a.
solve 25x^2-25x-6=0

1b.
the cost price of a diamond is $120000. Mary sold it to Helen at a profit of r%.
After one year, Helen sold the diamond back to Mary at a profit of r%.
As a result, Mary lost $28800. Find the value of r.

2.
The height of the perimeter of a right-angled triangle are x cm and 40cm
respectively. If the length of its base is 1cm less than twice its height, find the
value of x.


its quite difficult for me,,,,,, please help. Thanks a lot~
更新1:

for 1b, factor method should be used and ans should be r= 20 since r must be a positive value. r^2+100r-2400=0 (r+120)(r-20)=0 r= -120(rejected) or r= 20 Anyway, you did it well and i will give u the marks. Thanks~~~

回答 (1)

2010-09-15 4:28 am
✔ 最佳答案
1a)
25x^2-25x-6=0
(5x+1)(5x-6)=0
x=-1/5 or x=6/5

b)
The price which Mary sold to Helen
=120000(1+r/100)

The price which Helen sold back to Mary
=[120000(1+r/100)](1+r/100)
=120000(1+r/100)^2

Since Mary lost $28800, then:
120000(1+r/100)^2-120000(1+r/100)=28800
120000(1+r/100)(r/100)=28800
r^2+100r-2400=0
r=44.2 (corr. to 3 sig. fig.)

2)
Using the parameter of the tri. is 40cm
The slant height of the tri.=40-x-(2x-1)=41-3x

Then, by Pyth. Theorem:
(41-3x)^2=x^2+(2x-1)^2
1681-246x+9x^2=x^2+4x^2-4x+1
4x^2-242x+1680=0
x=52.5 (rejected) or x=8


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