6x^2-(1-3a)x-1/2a=0;
a. X1*X2=1/6;
b.X1=-1/X2;
c.0<X1*X2<1
6x^2-(1-3a)x-1/2a=0;
a. X1*X2=1/6;
b.X1=-1/X2;
c.0<X1*X2<1
6·x^2 - (1 - 3·a)·x - 1/2·a = 0
p = (- 1/2·a)/6-----> p = - a/12
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- a/12 = 1/6------> a = -2
verifica:
6·x^2 - (1 - 3·(-2))·x - 1/2·(-2) = 0
6·x^2 - 7·x + 1 = 0
x = 1/6 ∨ x = 1
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- a/12 = -1-------> a = 12
verifica:
6·x^2 - (1 - 3·12)·x - 1/2·12 = 0
6·x^2 + 35·x - 6 = 0
x = 1/6 ∨ x = -6
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{- a/12 > 0
{- a/12 < 1
quindi
{a < 0
{a > -12
quindi: [-12 < a < 0]