Q.

If a, b, c are non-zero real numbers such that

 01(1+cos8 x)(ax2+bx+c)dx=02(1+cos8 x)(ax2+bx+c)dx=0, then the equation ax2+bx+c=0 will have

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a

both the roots between 0 and 1

b

one root between 0 and 1 and other root between 1 and 2

c

both the roots between 1 and 2

d

both the roots between (3,  )

answer is A.

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Detailed Solution

01 f(x)=02 f(x) dx=0 01 f(x) dx=01 f(x) dx+12 f(x) dx   12 f(x)=0

 one root in (0, 1) and other root in (1, 2)

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