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The real number k for which the equation...

The real number k for which the equation, `2x^3+""3x""+""k""=""0` has two distinct real roots in [0, 1] (1) lies between 2 and 3 (2) lies between -1 and 0 (3) does not exist (4) lies between 1 and 2

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To solve the problem, we need to analyze the cubic equation given by: \[ f(x) = 2x^3 + 3x + k = 0 \] We want to find the values of \( k \) for which this equation has two distinct real roots in the interval \([0, 1]\). ### Step 1: Analyze the Function First, we need to find the derivative of the function \( f(x) \): ...
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