If $\int_{-2}^{-1}\left(a x^2-5\right) d x=0$ and $5+\int_1^2(b x+c) d x=0$, then

$a x^2-b x+c=0$ has atleast one root in $(1,2)$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

\int_{-2}^{-1}\left(a x^2-5\right) d x=0

and

5+\int_1^2(b x+c) d x=0

, then

View answer and explanation

Correct option: B

a x^2-b x+c=0

has atleast one root in

(-2,-1)

Option A (

g(x)

must be differentiable at

x=a

) is correct because for

f(g(x))

to be differentiable at

x=a

g(x)

must also be differentiable at

x=a

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