数学Paper 1讨论专区

Lov瑜瑜4ever

没有啊。。。他只是说p is the root..
   可是问题只PROVE f(x)
    x = 可以很多VALUE除了P以 ...
walrein_lim88 发表于 1-5-2010 10:01 PM

噢噢噢
那我还要和老师肯定下了
哈哈

永遠愛著許瑋倫

请问Ivanlsy 去哪里了？

永遠愛著許瑋倫

卡帖？

walrein_lim88

卡帖·～～～～～～～～～～～～

永遠愛著許瑋倫

Ivanlsy怎么像人间蒸发似的....

walrein_lim88

Ivanlsy怎么像人间蒸发似的....
永遠愛著許瑋倫 发表于 2-5-2010 01:26 PM

    你找他有事？？？

Lov瑜瑜4ever

已知a不等于b不等于c，求证a^2+b^2+c^2>ab+bc+ac

walrein_lim88

已知a不等于b不等于c，求证a^2+b^2+c^2>ab+bc+ac
Lov瑜瑜4ever 发表于 2-5-2010 01:59 PM

Lov瑜瑜4ever

噢噢噢
还有998楼pg40的也帮我看下
thx~

walrein_lim88

show that, for y不等于0, the polynomial p(y)=y^6-2y^5-4y^4+6y^3+4y^2-2y-1 can be expressed as
p(y)= ...
Lov瑜瑜4ever 发表于 1-5-2010 03:45 PM

   

乙劍真人

walrein_lim88 发表于 2-5-2010 03:27 PM

久没有来 STPM 专区，感觉自己的功力退步了..

walrein_lim88

久没有来 STPM 专区，感觉自己的功力退步了..
乙劍真人 发表于 2-5-2010 03:29 PM

    哪里会？？毕竟你是ADD MATHS老师，功力是不会退的。。。。
    可能很久没碰STPM吧～～，不过我相信你的能力很快的，功力会增加的！！

Lov瑜瑜4ever

Q1) Show that x^2-x+1 has the same sign for all values of x.

Q2) Show that as x changes, the maximum value of the function (a-x)(x-b) is
      1/4(a-b)^2.

Q3) Show that for all real values of a, the equation x^2+(3a-2)x+a(a-1)=0 has real roots for x.

Q4) Find the values of the expression
      5x^2-200x+1969
      as x changes between 0 and 50 inclusive

红字的那句到底是什么意思啊？

willyisstupid

回复 1013# Lov瑜瑜4ever


    a)用completing the square, you will get
       ( x - 1/4 )^2 + 3/4
       then
       x is real,
       ( x - 1/2 )^2 大过等于(use >= instead as below) 0
       ( x - 1/2 )^2 + 3/4 >= 3/4
       so the expression has the same sign(positive) for all real values of x
    b) ( a - x )( x - b )
= - ( x - a )( x - b )
= - [ x^2 -(a+b)x +ab ]
= - [ x - (a+b)/2 ]^2 + [(a+b)/2]^2 - ab
= - [ x - (a+b)/2 ]^2 + 1/4(a-b)^2
      因为这个是一个quadratic function ax^2 + bx + c with a>0,
      so the max value is 1/4(a-b)^2
    c) 我不是很确定，but try try
       post later
    d) let f(x) = 5x^2-200x+1969
        when x = - b/2a
                   = 20
      , that is axis of symmetry, min value is 5(20)^2 - 200(20) +1969 = - 31
       so f(0) = 1969 and f(50) = 4469
       therefore for 0<= x < 20 , 0>= f(x) > - 31 and for 20<= x <= 50 , -31<= f(x) <= 4469
       这只是suggested one , not sure XD
       anyone finds it's wrong please correct it, thanks..

Lov瑜瑜4ever

回复  Lov瑜瑜4ever


    a)用completing the square, you will get
       ( x - 1/4 )^2 + 3/4
   ...
willyisstupid 发表于 2-5-2010 09:02 PM

d)的看不是很懂
为什么要先找minimum point先的？

你现在在读者stpm？

walrein_lim88

Q1) Show that x^2-x+1 has the same sign for all values of x.

Q2) Show that as x changes, the maxi ...
Lov瑜瑜4ever 发表于 2-5-2010 06:20 PM

willyisstupid

回复 1015# Lov瑜瑜4ever


    因为你的graph最低点是你的min value
    不一定是when x=0 or x=50 的时候
    除非刚好 x=0 or x=50 is axis of symmetry or your quadratic function has a negative 'a'..

Lov瑜瑜4ever

回复  Lov瑜瑜4ever


    因为你的graph最低点是你的min value
    不一定是when x=0 or x=50 的时候 ...
willyisstupid 发表于 2-5-2010 09:22 PM

噢噢噢
明白了
哈哈
谢谢。。

數學神童

when a polynomial P(x) is divided by x^2-5x+6, the remainder is x+3. When P(x) is divided by x^2-6x+8, the remainder is 2x+1. Find the remainder when P(x) is divided by x^2-7x+12

walrein_lim88

when a polynomial P(x) is divided by x^2-5x+6, the remainder is x+3. When P(x) is divided by x^2-6x+ ...
數學神童 发表于 4-5-2010 03:19 PM