http://i8.photobucket.com/albums/a19/hunterxcurarpikt/11012007118.jpg
2007-01-11 13:52:27 · 4 個解答 · 發問者 ? 3 in 科學 ➔ 數學
圖片參考:http://i8.photobucket.com/albums/a19/hunterxcurarpikt/11012007118.jpg
(a)
f(x) = x2 + ax + b ... (*)
代 x = 1 至 (*),
f(1) = (1)2 + a(1) + b
f(1) = a + b + 1
代 x = 3 至 (*),
f(3) = (3)2 + a(3) + b
f(3) = 3a + b + 9
代 x = 4 至 (*),
f(4) = (4)2 + a(4) + b
f(4) = 4a + b + 16
===============================================
(b)
已知 f(1) = f(3),
a + b + 1 = 3a + b + 9
2a + 8 = 0
a = -4 .... (1)
已知 f(4) = 5,
4a + b + 16 = 5 【由 (a)】
4a + b + 11 = 0
4(-4) + b + 11 = 0 【由 (1)】
b - 5 = 0
b = 5 .... (2)
===============================================
(c)
若 f(x) = 2x
x2 + ax + b = 2x
x2 + (-4)x + (5) = 2x 【由 (1),(2)】
x2 - 4x + 5 = 2x
x2 - 6x + 5 = 0
(x-5)(x-1) = 0
x-5 = 0 或 x-1 = 0
x = 5 或 x = 1
2007-01-11 13:59:22 · answer #1 · answered by ? 6 · 0⤊ 0⤋
f(x) = x2 + ax + b
f(1) = (1)2 + a(1) + b = 1 + a + b
f(3) = (3)2 + a(3) + b = 9 + 3a + b
f(4) = (4)2 + a(4) + b = 16 + 4a + b
if f(4)=5 ; then 16 + 4a + b = 5 ;
f(1) = f(3) gives 1 + a + b = 9 + 3a + b
1 + a + b = 9 + 3a + b gives 1 + a = 9 + 3a and -2a = 8 and a = -4
put a = -4 into 16 + 4a + b = 5 gives 16 + 4(-4) + b = 5 and this gives b = 5 ;
f(x) becomes f(x) = x2 -4x + 5
When f(x) = 2x ; it gives x2 -4x + 5 = 2x
x2 -6x + 5 = 0
(x-5)(x-1) = 0
x=5 or x=1
2007-01-11 14:09:48 · answer #2 · answered by ? 7 · 0⤊ 0⤋
a)
f(1)=1+a+b
f(3)=9+3a+b
f(4)=16+4a+b
b)
f(1)=f(3)
1+a+b=9+3a+b
-8=2a
a=-4
f(4)=5
16+4a+b=5
16-16+b=5
b=5
c)
if f(x)=2x
x^2-4x+5=2x
x^2-6x+5=0
(x-5)(x-1)=0
x=5 or x=1
2007-01-11 14:06:24 · answer #3 · answered by KY Wong 2 · 0⤊ 0⤋
f(x)=x^2+ax+b
a.
f(1)=1^2+1a+b
=a+b+1
f(3)=3^2+3a+b
=3a+b+9
f(4)=4^2+4a+b
=4a+b+16
b.
∵ f(1)=f(3)
∴a+b+1=3a+b+9
a-3a+b-b=9-1
-2a=8
∴a=-4
∵f(4)=5
∴4a+b+16=5
b=5-16-4a
b=-11-4a
b=-11-4(-4)
b=-11+16
∴b=5
∴a=-4,b=5
c.
f(x)=2x
x^2+ax+b=2x
x^2-4x+5=2x
x^2-6x+5=0
x=[ 6 ± √[ (-6)^2 - 4(1)(5) ] ]/2
=[6±√(36-20) ]/2
=(6±√16)/2
=(6±4)/2
=5 or 1
2007-01-11 14:02:23 · answer #4 · answered by ? 6 · 0⤊ 0⤋