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書.有咩唔名就應該問呀sir. |
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 |
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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