IIT JEE , AIEEE Forum - Mathematics , Algebra

ashish_banga

If 19a + 5b + c = 0 then at least one root of equation 3ax^2 + 2bx + c = 0
will be in the interval
(A) (1,2)
(B) (-1,2)
(C) (2,3)
(D) (0,1)

feynmann

ans> C ( 2, 3 )

proof :

consider the fn f( x ) = ax^3 + bx^2 + cx

now note that f( 2 ) = f(3 ) ( using the given equality ) and f( x ) is clearly differentiable in [2,3]

hence by Rolle's theorem , there must be a root of f'(x ) = 3ax^2 + 2bx + c =0 in the interval ( 2,3 )