Suppose the cubic \( x^{3}-p x+q=0 \) has three distinct real roots...

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Suppose the cubic \( x^{3}-p x+q=0 \) has three distinct real roots, where \( p0 \) and \( q0 \). Which one of the following
P holds?
[AIEEE 2008, 3M]
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(a) The cubic has minima at \( \left(-\sqrt{\frac{p}{3}}\right) \) and maxima at \( \sqrt{\frac{p}{3}} \)
(b) The cubic has minima at both \( \sqrt{\frac{p}{3}} \) and \( \left(-\sqrt{\frac{p}{3}}\right) \)
(c) The cubic has maxima at both \( \sqrt{\frac{p}{3}} \) and \( \left(-\sqrt{\frac{p}{3}}\right) \)
(d) The cubic has minima at \( \sqrt{\frac{p}{3}} \) and maxima at \( \left(-\sqrt{\frac{p}{3}}\right) \)
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