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Suppose the cubic x^(3) - px + q has thr...

Suppose the cubic `x^(3) - px + q` has three distinct real roots where `p gt 0 and q gt 0`. Then which one of the following holds ?

A

The cubic has a minimum at `sqrt(p//3)` and a maximum at `-sqrt(p//3)`.

B

The cubic has a minimum at `-sqrt(p//3)` and a maximum at `sqrt(p//3)`.

C

The cubic has minima at both `sqrt(p//3) and -sqrt(p//3)`.

D

The cubic has maxima at both `sqrt(p//3) and -sqrt(p//3)`.

Text Solution

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The correct Answer is:
A
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