IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

neeraj_agarwal_1990

Let f(x) be (ax^3)/3 + (bx^2)/2 +cx

f(1) = a/3 +b/2 +c = (2a+3b+6c)/6 =0....(given)
f(0)=0

and since it is an algebric function...its differentiable and continuous in R....

it satisfies all conditions for rolle's thm....for x in (0/1)

so there lies at least one x for which f ' (x) =0 in (0,1)

so there is at least 1 x for which ax^2 +bx+c=0

Its a general approach for such questions in which we assume f(x) as the integral of the required function..

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