If the equation ` 2x^(3) -6x + k=0` has three real and distinct roots, then find the value (s) of k.

Explanation

let ` f(x) = 2x^(3) - 6x = k Rightarrow f(x) = 6x^(2) -6`
if f'(x) = 0 then ` x = +-1`
For three distinct real roots.
f(1) f(-1) ` lt Rightarrow (k-4) ( k + 4) lt 0`
` Rightarrow -4 lt k lt 4`