【纪念当年的帖子（2010）】Add Maths功课讨论区

×寂寞°心

sketch the graph f(x)=|3-2x| for 0≦x≦3.Determine the range of values of f in the given domain.
这题是要我画东西是吗？画什么?@@

×寂寞°心

有人吗？

乙劍真人

sketch the graph f(x)=|3-2x| for 0≦x≦3.Determine the range of values of f in the given domain.
这 ...
×寂寞°心 发表于 18-1-2011 03:28 PM

你先不要管那个 modulus，如果你的答案是 -ve ，换成 +ve 就对了

x       0        1        2        3      
f(x)    3        1        1        3

然后自己 plot 那个 graph.. 你的图如果是一个 V shape 就对了..

×寂寞°心

if the roots of the quadration x^2+(n-2)x+m=0 are 2 and 4 ,find the values of m and n ....
这题怎么做？？
chapter 2 的～～

Allmaths

if the roots of the quadration x^2+(n-2)x+m=0 are 2 and 4 ,find the values of m and n ....
这题怎么 ...
×寂寞°心 发表于 24-1-2011 06:43 PM

用S.O.R和P.O.R

S.O.R, 2+4=-(n-2)
              6=2-n
              n=-4
P.O.R, 2(4)=m
             m=8

×寂寞°心

1）if a and b are the roots of the equation x^2-4x+6=0 , find the equation whose roots are:
a) [α+(1/β)] and [β+(1/α)]
这题好复杂....

2）One root of the equation 2x^2-4x+p=0 is three times the other. Find the value of P.

3）form the quadratic equation whose are shown below.
a)2+(square root of 3)and2-(square root of 3)
因为没有square root of这个符号...我就用写的

4）the roots of the equation x^2+px+q=0 are m and 3m.Show that 3p^2=16q

Allmaths

1）if a and b are the roots of the equation x^2-4x+6=0 , find the equation whose roots are:
a) [α+ ...
×寂寞°心 发表于 24-1-2011 10:11 PM

   
S.O.R, α+β=4
P.O.R,   αβ=6

[α+(1/β)]+[β+(1/α)]=α+β+1/α+1/β
                            =α+β+(α+β)/αβ
                            =4+(4/6)
                            =14/3

[α+(1/β)][β+(1/α)]=αβ+(1/αβ)+2
                          =6+(1/6)+2
                          =49/6

New equation:
x^2-(14/3)x+(49/6)=0
         6x^2-28x+49=0

Allmaths

2）One root of the equation 2x^2-4x+p=0 is three times the other. Find the value of P.
×寂寞°心 发表于 24-1-2011 10:11 PM

2x^2-4x+p=0
x^2-2x+(p/2)=0

let @ to be one of the roots to the equation.

@+3@=2
     4@=2
       @=1/2

@(3@)=p/2
3@^2=p/2
p/2=3(1/2)^2
p=3/2

3）form the quadratic equation whose are shown below.
a)2+√3 and 2-√3

S.O.R=2+√3+2-√3
        =4

P.O.R=(2+√3)(2-√3)
       =1

Quadratic equation:
x^2-(S.O.R)x+(P.O.R)=0
                 x^2-4x+1=0

4）the roots of the equation x^2+px+q=0 are m and 3m.Show that 3p^2=16q

x^2+px+q=0

S.O.R, m+3m=-p
               4m=-p
                m=-p/4   ---eq 1

P.O.R, m(3m)=q
           3m^2=q       ---eq 2

Sub eq 1 into eq 2,
3(-p/4)^2=q
(3p^2)/16=q
       3p^2=16q   (shown)

×寂寞°心

=α+β【+1/α+1/β】
=α+β【+(α+β)/αβ】<----
本来不是+1/α+1/β的吗？
为什么会变成+（α+β）/αβ呢？？

Allmaths

=α+β【+1/α+1/β】
=α+β【+(α+β)/αβ】
×寂寞°心 发表于 24-1-2011 10:44 PM

1/α+1/β=β/(αβ)+α/(αβ)
           =(α+β)/αβ

×寂寞°心

我终于懂第二题了。。我先睡了
我明天再来研究
谢谢allmaths哦

×寂寞°心

再问一个问题下。。。
P.O.R=(2+√3)(2-√3)
       =1
为什么会等于1？

Allmaths

再问一个问题下。。。
P.O.R=(2+√3)(2-√3)
       =1
为什么会等于1？
×寂寞°心 发表于 24-1-2011 11:02 PM

   
expand 它就可以了。。。

(2+√3)(2-√3)=4-2√3+2√3-3
                   =4-3
                   =1

×寂寞°心

哦哦～懂了懂了
谢谢哦～
我去睡了^^

×寂寞°心

given that the quadratic equation is (2m+3)x^2+(4m-2)x-(m+1)=0.Find the values of m, if
a)one of the root of the equation is negative
b)one fo the root of the equation is reciprocal of the other
这题不懂

×寂寞°心

没人吗

peaceboy

回复 795# ×寂寞°心


    given that the quadratic equation is (2m+3)x^2+(4m-2)x-(m+1)=0.Find the values of m, if
a)one of the root of the equation is negative


c/a<0

-(m+1)/ (2m+3)<0
-3/2<m<-1


b)one fo the root of the equation is reciprocal of the other
c/a =1
-(m+1)/ (2m+3)=1
(2m+3)=-(m+1)
2m+3+m+1=0
m= - 4/3

×寂寞°心

Business~
1)Hamadan bought x number of calculators for RM704.He sold 20 of them at a profit of RM6 each.
(a)Write down an expression,in terms x,for the selling price of each calculator .
(b)Hamadan sold the remaining calculators at RM30 each .Write down in terms of x ,the total amount of money he receive for all the calculators.
(c)Given that hamadan received RM920 altogether,form an equation in x and show that it reduces to 3x^2-140x+1408=0.
(d)Solve the equation and hence find the number of calculators Hamadan bought.

Sport~
2)During a training session for the 2006 Doha,Asian Games,Kim Chong cycled 60Km form Ayer Hitam to Pagoh at a uniform speed of x km h-1.If he had increase his speed by 10km h-1,he would have had arrive at Pagoh half an hour earlier.
(a)Form an equation in x and show that it reduces to x^2+10x-1200=0.
(b)Solve this equation to find Kim Chong original speed.

这两题干长

×寂寞°心

有人懂做吗？

Allmaths

Business~
2)During a training session for the 2006 Doha,Asian Games,Kim Chong cycled 60Km form Ayer Hitam to Pagoh at a uniform speed of x km h-1.If he had increase his speed by 10km h-1,he would have had arrive at Pagoh half an hour earlier.
(a)Form an equation in x and show that it reduces to x^2+10x-1200=0.
(b)Solve this equation to find Kim Chong original speed.
×寂寞°心 发表于 30-1-2011 02:22 PM

   
(a)(60/x)-[60/(x+10)]=0.5
       2[60(x+10)-60x]=x(x+10)
                       1200=x^2+10x
          x^2+10x-1200=0

(b)x^2+10x-1200=0
       (x-30)(x+40)=0
    x=30   or   x=-40(rejected)

original speed, x=30 km/h