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

Step-by-step solution

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.