MQ41 --- Roots

ax³ + bx² + cx + d = 0α + β + γ = - b/a ... (1)
αβ + βγ + γα = c/a ... (2)
αβγ = - d/a ... (3)(2) / (3) :
(αβ + βγ + γα) / (αβγ) = 1/α + 1/β + 1/γ = - c/d(1) / (3) :
(α + β + γ ) / (αβγ) = 1/(αβ) + 1/(βγ) + 1/(γα) = b/d1 / (3) :
1 / (αβγ) = - a/dSo the roots of dx³ + cx² + bx + a = 0 are 1/α , 1/β , 1/γ.

2012-09-04 18:42:24 補充：
Alternatively :

ax³ + bx² + cx + d = 0
(ax³ + bx² + cx + d) / x³ = 0
d(1/x)³ + c(1/x)² + b(1/x) + a = 0

So the roots of dx³ + cx² + bx + a = 0 are 1/α , 1/β , 1/γ.

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