Consider an unknown polynomial which when divided by \( (x-3) \) and \( (x-4) \) leaves remainde...

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Consider an unknown polynomial which when divided by \( (x-3) \) and \( (x-4) \) leaves remainders 2 and 1 , respectively. Let \( R(x) \) be the remainder when this polynomial is divided by \( (x-3)(x-4) \)
Range of \( f(x)=[R(x)] /\left(x^{2}-3 x+2\right) \) is
(a) \( [-2,2] \)
(b) \( (-\infty,-2-\sqrt{3}] \cup[-2+\sqrt{3}, \infty) \)
(c) \( (-\infty,-7-4 \sqrt{3}] \cup[-7+4 \sqrt{3}, \infty) \)
(d) none of these
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