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Quadratic Inequality

Source: 1998 National High School Mathematics League, Exam One, Problem 4

March 9, 2020

inequalities

Problem Statement

Statement

P

: solution set to inequalities

a_1x^2+b_1x+c_1>0

and

a_2x^2+b_2x+c_2>0

are the same; statement

Q

:

\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}

.

\text{(A)}

\text{(D)}

is sufficient and necessary condition of

P

.

\text{(B)}

Q

is sufficient but unnecessary condition of

P

.

\text{(C)}

Q

is insufficient but necessary condition of

P

.

\text{(D)}

Q

is insufficient and unnecessary condition of

P

.

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