Let .
For three distinct roots between 0 and 1 , the cubic must change sign inside the interval at least twice

• Critical points

Critical points: .

Inside , so is strictly decreasing on .

• Consequence

A strictly decreasing function can cross the -axis only once in that interval.
Hence it cannot have three distinct roots between 0 and 1 for any value of .
Therefore no given value of satisfies the condition.

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