Entries of Column I are to be matched with one or more entries of Column II

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Entries of Column I are to be matched with one or more entries of Column II.

Column I	Column II
(a) If $a+b+2c=0$ and $c\ne0$ , then $ax^2+bx+c=0$ has	(p) At least one root in $(-2,0)$
(b) If $a,b,c\in\mathbb{R}$ such that $2a-3b+6c=0$ , then $ax^2+bx+c=0$ has	(q) At least one root in $(-1,0)$
(c) Let $a,b,c$ be non-zero real numbers such that $\int_0^1(1+\cos^8x)(ax^2+bx+c)\,dx=\int_0^2(1+\cos^8x)(ax^2+bx+c)\,dx$ . Then $ax^2+bx+c=0$ has	(r) At least one root in $(-1,1)$
	(s) At least one root in $(0,1)$
	(t) At least one root in $(0,2)$