THETA DIVISION

Question 99

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Question

Questions #10-12 all concern the same quadratic. Given

f(x)=ax^2+bx+c

where

a,b,c\in\mathbb Z

, which of the following must be true?

\begin{array}{ll} \text{I.} & \text{The sum of the roots is an integer.}\\ \text{II.} & \text{The roots are integers.}\\ \text{III.} & f(x)\text{ is defined for all integer values of }x. \end{array}

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Question

Questions #10-12 all concern the same quadratic. Given

f(x)=ax^2+bx+c

where

a,b,c\in\mathbb Z

, which of the following must be true?

\begin{array}{ll} \text{I.} & \text{The sum of the roots is an integer.}\\ \text{II.} & \text{The roots are integers.}\\ \text{III.} & f(x)\text{ is defined for all integer values of }x. \end{array}