2013-2-27 05:57 PM
ch1997jimmy
又係數學功課 求解!!!~
其實都計到開頭不過之後就唔係好識.
第1-3,6,7都識小小既,其他就...
1.當x^2+mx+5除以x-1時,商式是x+2,餘式是5.求m的值.
2.當2x^2+mx+p除以2x+1時,商式是x-5,餘式是7.求m和p的值.
3.當3x^2+mx-6除以x-2時,商式是3x+p,餘式是2,求m和p的值.
之後係餘式定理.
4.(x^2+5x-6)除(x-2)
5.(x^3-5x^2+6x+5)除(x+3)
6.當f(x)=x^3+3x^2+k除以(x-2)時,餘式是5,求k的值.
7.當f(x)=2x^3+kx^2+5x-3除以(x+1)時,餘式是5.求k的值.
8.當f(x)=x^3-4x^2+hx+k除以(x-1)和(x+3)時,餘式分別是4和-76.求h和k的值.
唔知有冇人解決.我都知唔可以一未靠人既.我E家都有聽書架.
我覺得數學冇得自己温書.有咩唔名就應該問呀sir.
2013-2-27 06:05 PM
keith_keith
1. x^2 + mx + 5 = (x - 1) (x + 2) + 5
2. 2x^2 + mx + p = (2x + 1) (x - 5) + 7
3. 3x^2 + mx - 6 = (x - 2) (3x + p) + 2
4. sub x = 2, i.e. (2)^2 + 5(2) - 6
5. sub x = -3, i.e. (-3)^3 - 5(-3)^2 + 6(-3) +5 注意負號
6. f(x)=x^3 + 3x^2 + k除以(x-2)時,餘式是5, i.e. f(2) = 5 -> (2)^3 + 3(2)^2 + k = 5
7. f(x)=2x^3 + kx^2 + 5x - 3除以(x+1)時,餘式是5, i.e. f(-1) = 5 -> 2(-1)^3 + k(-1)^2 + 5(-1) - 3 = 5
8. f(x)=x^3 - 4x^2 + hx + k除以(x-1)和(x+3)時,餘式分別是4和-76, i.e. f(1) = 4 -> (1)^3 - 4(1)^2 + h(1) + k = 4
f(-3) = -76 -> (-3)^3 - 4(-3)^2 + h(-3) + k = -76
then solving equation, 自己計
2013-2-27 06:22 PM
hh36471288hk
[quote][b]原帖由 [i]ch1997jimmy[/i] 於 2013-2-27 05:57 PM 發表。 [/b][url=http://forum.eyankit.com/viewthread.php?tid=89464&page=1#pid969161][img]http://forum.eyankit.com/images/common/back.gif[/img][/url]
其實都計到開頭不過之後就唔係好識.
第1-3,6,7都識小小既,其他就...
2.當2x^2+mx+p除以2x+1時,商式是x-5,餘式是7.求m和p的值.
3.當3x^2+mx-6除以x-2時,商式是3x+p,餘式是2,求m和p的值.
之後係餘式定理.
4.(x^2+5x-6)除(x-2)
5.(x^3-5x^2+6x+5)除(x+3)
6.當f(x)=x^3+3x^2+k除以(x-2)時,餘式是5,求k的值.
7.當f(x)=2x^3+kx^2+5x-3除以(x+1)時,餘式是5.求k的值.
8.當f(x)=x^3-4x^2+hx+k除以(x-1)和(x+3)時,餘式分別是4和-76.求h和k的值.
唔知有冇人解決.我都知唔可以一未靠人既.我E家都有聽書架.
我覺得數學冇得自己温書.有咩唔名就應該問呀sir.[/quote]
[b]1.當x^2+mx+5除以x-1時,商式是x+2,餘式是5.求m的值.[/b]
1. x^2+mx+5 = (x-1)(x+2)+5
.....
你之後應該識掛.... :em16:
[b]當2x^2+mx+p除以2x+1時,商式是x-5,餘式是7.求m和p的值.[/b]
2. 2x^2+mx+p = (2x+1)(x-5)+7
2x^2+mx+p = 2x^2 -10x +x -5 +7
2x^2+mx+p = 2x^2 -9x +2
你之後應該識掛.... :em16:
[b]3.當3x^2+mx-6除以x-2時,商式是3x+p,餘式是2,求m和p的值.[/b]
3. 3x^2+mx-6 = (x-2)(3x+p)+2
.....
同上一樣做法
[b]4. (x^2+5x-6) / (x-2)[/b]
.....
上次做過, 請參考 :em16:
[b]5. (x^3-5x^2+6x+5) / (x+3)[/b]
.....
同上:em16:
[b]6.當f(x)=x^3+3x^2+k除以(x-2)時,餘式是5,求k的值.[/b]
6. f(x)=x^3+3x^2+k
袋f(x) = 0
F(x) = x-2
0 = x-2
x = 2
f(2) = x^3+3x^2+k
5 = (2)^3 + 3(2)^2 +k
5 = 8+12+k
5 = 20+k
5-20 = k
-15 = k //
[b]7.當f(x)=2x^3+kx^2+5x-3除以(x+1)時,餘式是5.求k的值.[/b]
7. f(x)=2x^3+kx^2+5x-3
袋f(x) = 0
f(x) = x+1
0 = x+1
x = -1
f(-1) = 2x^3+kx^2+5x-3
5 = 2(-1)^3+k(-1)^2+5(-1)-3
5 = -2+k-5-3
5 = -11+k
16 = k //
[b]8.當f(x)=x^3-4x^2+hx+k除以(x-1)和(x+3)時,餘式分別是4和-76.求h和k的值.[/b]
仆_ :em141:
WTFFFF 聯立方程 Fuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu
let me try it :em16:
[color=DimGray]f(x)=x^3-4x^2+hx+k
袋f(x) = 0
0 = x-1
x = 1 ---- (1)
f(x)=x^3-4x^2+hx+k
袋f(x) = 0
0 = x+3
x = -3 ---- (2)
f(1)=x^3-4x^2+hx+k
4 = (1)^3 -4(1)^2 +h(1)+k
4 = 1 -4 +h +k
7 = h +k
f(-3)=x^3-4x^2+hx+k
-76 = (-3)^3 -4(-3)^2 +h(-3) +k
-76 = -27 -36 -3h +k
-13 = -3h +k[/color]
此有待高手解答 :clown::em16:
2013-2-27 10:34 PM
keith_keith
回覆 #3 hh36471288hk 的帖子
8. f(x)=x^3 - 4x^2 + hx + k除以(x-1)和(x+3)時,餘式分別是4和-76,
i.e. f(1) = 4 -> (1)^3 - 4(1)^2 + h(1) + k = 4
1 - 4 + h + k = 4
h + k = 7 ---------------------(1)
f(-3) = -76 -> (-3)^3 - 4(-3)^2 + h(-3) + k = -76
-27 - 36 - 3h + k = -76
-3h + k = -13 -------------(2)
(1) - (2), h + k - (-3h + k) = 7 - (-13)
4h = 20
h = 5
k = 2
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