The real number k for which the equation, 2x3+3x+k=0 has two distinct real roots in \[\left[ {0,\,1} \right]\]
Solutions · 1
Official solution
\[f\left( x \right) = 2{x^3} + 3x + k\]
\[f'\left( x \right) = 6{x^2} + 3 > 0\]
\[\forall x \in R\] \[\,\,\,\,\,\,\] (as \[\,\,\,\,\,\,\] x2>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.