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Let a, b, c be non-zero real numbers suc...

Let `a, b, c` be non-zero real numbers such that ; `int_0^1 (1 + cos^8 x)(ax^2 + bx + c)dx = int_0^2 (1+cos^8 x)(ax^2 + bx +c)dx` then the quadratic equation `ax^2 + bx + c = 0` has -

A

No root in (0, 2)

B

At least one root in (0, 2)

C

A double root in (0, 2)

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
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Statement-1: Let a,b,c be non zero real numbers and f(x)=ax^2+bx+c satisfying int_0^1 (1+cos^8x)f(x)dx=int_0^2(1+cos^8x)f(x)dx then the equation f(x)=0 has at least one root in (0,2) .Statement-2: If int_a^b g(x)dx vanishes and g(x) is continuous then the equation g(x)=0 has at least one real root in (a,b) . (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true