JEE Previous Year Question
The real number k for which the equation, 2x3 + 3x + k = 0 has two distinct real roots in [0, 1]
Topic: JEE PYQ
Answer: D. Full step-by-step solution below.
- Alies between 1 and 2
- Blies between 2 and 3
- Clies between –1 and 0
- Ddoes not exist.
Correct answer: D
Solution
(d)f(x) = 2x3 + 3x + kf′(x) = 6x2 + 3 > 0 ∀ x ∈ R
⇒ f(x) is strictly increasing function
⇒ f(x) = 0 has only one real root, so two roots are not possible