Theory of Equations 5 Question 4
4. The real number $k$ for which the equation, $2 x^{3}+3 x+k=0$ has two distinct real roots in $[0,1]$
(2013 Main)
(a) lies between 1 and 2
(b) lies between 2 and 3
(c) lies between -1 and 0
(d) does not exist
Show Answer
Solution:
- Let $f(x)=2 x^{3}+3 x+k$
On differentiating w.r.t. $x$, we get
$$ f^{\prime}(x)=6 x^{2}+3>0, \forall x \in R $$
$\Rightarrow f(x)$ is strictly increasing function.
$\Rightarrow f(x)=0$ has only one real root, so two roots are not possible.
