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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

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Let f(x)=`x^(3)-3x+a`
lf f(x) =0, then `3x^(2)-3=0rArrx=opluse1`
For three distinict roots ,`f(1)xxf(-1)lt0`
`(1-3+a)(-1+3+a)lt0`
`(a+2)(a-2)lt0`
`-2ltalt2`
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