QJEEM13Ma9bab: JEE Main 2013 Mathematics - Class 12 JEEM13Ma9bab Solution: The real number for which the equation, has two distinct real…

Question

Verified Solution • 2025–26 Session moderate

The real number

k

for which the equation,

2{x^3} + 3x + k = 0

has two distinct real roots in

\left[ {0,\,1} \right]

Accepted Answer

f\left( x \right) = 2{x^3} + 3x + k

f'\left( x \right) = 6{x^2} + 3 &gt; 0

\forall x \in R

\,\,\,\,\,\,

(as

\,\,\,\,\,\,

{x^2} &gt; 0

)

\Rightarrow f\left( x \right)

is strictly increasing function

\Rightarrow f\left( x \right) = 0

has only one real root, so two roots are not possible.

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