If , , and are non-zero real numbers such that , then the equation will…

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

a

b

, and

c

are non-zero real numbers such that

\int_0^1(1+\cos^6x)(ax^2+bx+c)\,dx=0

, then the equation

ax^2+bx+c=0

will have (1) one root between

0

and

1

and another between

1

and

2

(2) both roots between

0

and

1

(3) both roots between

1

and

2

(4) None of the above