Application of DerivativeHard

Question

The real number k for which the equation 2x3 + 3x + k = 0 has two distinct real roots in [0, 1]

Options

A.lies between 1 and 2.
B.lies between 2 and 3.
C. lies between -1 and 0
D.does not exist

Solution

        f(x) = 2x3 + 3x + k
        f′(x) = 6x2 + 3 > 0
⇒      f is increasing function
⇒      f (x) = 0 has exactly one real root.  (as it is an odd degree polynomial)

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