THETA DIVISION

Question 108

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Question

The following questions (#18-19) consider the function

h(x)=\frac{ax^2+bx+c}{x^2-2x-35},\qquad a,b,c\in\mathbb Z.

If it is known that

h(x)

has exactly one removable discontinuity, which of the following could be true?

\begin{array}{ll} \text{I.} & c\text{ is divisible by 7 but is not divisible by 5}\\ \text{II.} & c\text{ has a 0 as its units digit}\\ \text{III.} & c\text{ is divisible by both 7 and 5} \end{array}

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Question

The following questions (#18-19) consider the function

h(x)=\frac{ax^2+bx+c}{x^2-2x-35},\qquad a,b,c\in\mathbb Z.

If it is known that

h(x)

has exactly one removable discontinuity, which of the following could be true?

\begin{array}{ll} \text{I.} & c\text{ is divisible by 7 but is not divisible by 5}\\ \text{II.} & c\text{ has a 0 as its units digit}\\ \text{III.} & c\text{ is divisible by both 7 and 5} \end{array}