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If the equation 2x^(3) -6x + k=0 has t...

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

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To find the values of \( k \) for which the equation \( 2x^3 - 6x + k = 0 \) has three real and distinct roots, we will follow these steps: ### Step 1: Differentiate the function We start with the function: \[ f(x) = 2x^3 - 6x + k \] Now, we differentiate \( f(x) \) to find the critical points: ...
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