Question

The real number k for which the equation, $2x^3+3x+k=0$ has two distinct real roots in [0, 1]

• A. lies between 1 and 2
• B. lies between 2 and 3
• C. lies between – 1 and 0
• D. does not exist

Answer 1

The correct option is D does not exist

Let $f\left(x\right)=2x^3+3x+k$
On dofferentiating w.r.t. x,
we get $F^{\prime }\left(x\right)=6x^2+3>0,\forall x\in R$
$\Rightarrow$ f(x) is strictly increasing function.
$\Rightarrow$ f(x) = 0 has only one real root, so two roots are not possible.