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

Question

The real number k for which the equation, 2 x 3 + 3 x + k = 0 has two distinct real roots in [ 0 , 1 ] belongs to, lies between - 1 and 0 ., does not exist., lies between 1 and 2 ., lies between 2 and 3 .

MARKS App · Accepted Answer

Given f x = 2 x 3 + 3 x + x ⇒ f ' x = 6 x 2 + 3 As f ' x > 0 for all x . ⇒ f x is a strictly increasing function for all x . Hence f x = 0 cannot have more than one root.

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