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Plz explain sir the concept of approaching this type of problems:- The real number K for which the equation 2 x³ + 3 x + K = 0 has two distinct real roots in [0,1]:- 1. lies between 1 and 22. lies between 2 and 33. lies between -1 and 04. does not exist

Plz explain sir the concept of approaching this type of problems:- The real number K for which the equation 2 x³ + 3 x + K = 0 has two distinct real roots in [0,1]:- 1. lies between 1 and 22. lies between 2 and 33. lies between -1 and 04. does not exist

Grade:12th pass

1 Answers

Arun
25750 Points
6 years ago
Dear Sohan
 
Correct option will be (d)
f(x) = 2x3 + 3x + kf′(x) = 6x2 + 3f′(x) = 0
⇒ x2 = -1/2
Not Possible.
As condition for two distinct real root is f(α) f(β) = 0
(where α, β are roots of f '(x) = 0 )
 
Regards
Arun (askIITians forum expert)

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