Let \( p, q \) be non-zero, real numbers and \( x_{1}, x_{2}, x_{3}...

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Let \( p, q \) be non-zero, real numbers and \( x_{1}, x_{2}, x_{3} \) be the roots of \( x^{3}+p x+q=0 \) such that \( x_{3}=\frac{1}{x_{1}}+\frac{1}{x_{2}} \), then
(a) \( q \) is a root of \( x^{2}+p x+q=0 \)
(b) \( q0 \)
(c) \( p0 \)
(d) \( x_{1}+x_{2}0 \)
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