If f ( x ) = a x 3 + b x 2 + c x + d , ( a , b , c , d are rational) and roots of f ( x ) = 0 are eccentricities of a parabola and a rectangular hyperbola then a + b + c + d equals

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Roots of f ( x ) are 1 , 2 ​ , − 2 ​ ​ a x 3 + b x 2 + c x + d = ( x − 1 ) ( x − 2 ​ ) ( x + 2 ​ ) = ( x − 1 ) ( x 2 − 2 ) = x 3 − x 2 − 2 x + 2 ​ ​ a = 1 , b = − 1 , c = − 2 , d = 2 ⇒ a + b + c + d = 0

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