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Suppose the cubic x^3-px+q has three rea...

Suppose the cubic `x^3-px+q` has three real roots where `pgt0` and `qgt0` . Then which one of the following holds ?
1) The cubic has minimum at both √p/3 and −√p/3
2) The cubic has maximum at both √p/3 and −√p/3
3)The cubic has minimum at √p/3 and maximum at −√p/3
4)The cubic has minimum at −√p/3 and maximum at √p/3

A

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

B

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

C

The cubis has minimum at `sqrt(p/3)` and maximum at `-sqrt(p/3)`

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
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