[ 數學 ]二項式nCr

1. n=6 , a=-1
2. a=2 , c=-4

2009-06-07 22:45:51 補充：

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2.
根之和 = -7/2
-7/a=-7/2
a=2

根之積= -2
c/a=-2
c/2=-2
c=-4

(1+ x )^n (4 + 2x ^2 + ax^3 ) = 4+ 24x + 62x^2 + 91x^3 +...
(1+x)^n (4+2x^2+ax^3)
=(1+ nC1 x+ nC2 x^2 + nC3 x^3 + .... )(4+2x^2+ax^3)
=[1+nx+n(n-1)/2 x^2 + n(n-1)(n-2) / 6 x^3 + ...)(4+2x^2+ax^3)
=4 + 4nx + 4n(n-1)/2 x^2 + 4n(n-1)(n-2)/6 x^3 + 2x^2 + 2nx^3 + ax^3 +...
=4 + 4nx + 4n(n-1)/2 x^2 + 2x^2 + 4n(n-1)(n-2)/6 x^3 + 2nx^3 + ax^3 +....
=4 + 4nx + [4n(n-1)/2 + 2]x^2 + [4n(n-1)(n-2)/6 + 2n + a] x^3
∴4n = 24
n = 6
4n(n-1)(n-2)/6 + 2n + a = 91
4x6(5)(4)/6 + 2(6) + a = 91
92 + a = 91
a = -1
2. α + β = -7/a = -7/2
a = 2
αβ = c/a = -2
c/2 = -2
c = -4