Question

If the equation $x ^3-12 x + a =0$ has exactly one real root, then range of a is equal to

• A. $(-\infty,-16) \cup(16, \infty)$
• B. $\{-16,16\}$
• C. $(-16,16)$
• D. $(-\infty,-16] \cup[16, \infty)$

Answer 1

Answer: (A)

Let $y=f(x)=x^3-12 x$ and $y=-a$
For $f(x)=-a$ to have exactly one real root, we must have
$-a >16 \text { or }-a<-16 $
$\Rightarrow a \in(-\infty,-16) \cup(16, \infty)$