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 \( (x-3)(x-4) \)
If equation \( R(x)=x^{2}+a x+1 \) has two distinct real roots, then exhaustive values of \( a \) are
(a) \( (-2,2) \)
(b) \( (-\infty,-2) \cup(2, \infty) \)
(c) \( (-2, \infty) \)
(d) all real numbers
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