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

Engineering

Mathematics

Roots of a Cubic

Question

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

lies between 1 and 2.

lies between – 1 and 0.

does not exist

lies between 2 and 3

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f (x) = 2x³ + 3x + k

f ' (x) = 6x² + 3

f ' (x) is always positive, hence f (x) is an increasing function

i.e. f (x) has only one real root.