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Find the value of a if x^3-3x+a=0 has th...

Find the value of `a` if `x^3-3x+a=0` has three distinct real roots.

Text Solution

Verified by Experts

The correct Answer is:
`-2 lt a lt 2`
Let `f(x) = x^(3) - 3x = a`
Let `f'(x) = 0`
`rArr 3x^(2) - 3 = 0 or x = pm 1`

For three distinct roots , `f(1) lt 0 and f (-1) gt 0`
`rArr 1 -3 + a lt 0 and - 1 + 3 + a gt a`
or `a lt 2 and a gt - 2`
or ` - 2 lt a lt 2`
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