JEE Advance - Mathematics (2001 - No. 10)
Let $$ - 1 \le p \le 1$$. Show that the equation $$4{x^3} - 3x - p = 0$$
has a unique root in the interval $$\left[ {1/2,\,1} \right]$$ and identify it.
has a unique root in the interval $$\left[ {1/2,\,1} \right]$$ and identify it.
The equation has no root in the interval [1/2, 1]
The equation has multiple roots in the interval [1/2, 1]
The unique root is x = cos(arccos(p)/3)
The unique root is x = sin(arcsin(p)/3)
The unique root is x = tan(arctan(p)/3)
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