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

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

Text Solution

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Let `f(x)=x^(3)-3x+a`
Let `f'(x)=0`
`rArr 3x^(2)-3=0 rArr x=+-1`
For three distinct roots, `f(1)*f(-1) lt 0`
`rArr (1-3+a)(-1+3+a) lt 0`
`rArr (a-2)(a+2)lt 0`
`rArr -2 lt a lt 2`
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