June 5th, 2017, 01:48 AM  #1 
Senior Member Joined: Nov 2015 From: hyderabad Posts: 242 Thanks: 4  Empty set
If $\displaystyle f : R \rightarrow R$ is a cubic polynomial then $\{x \in R : f(x^3) = \sqrt2\}$ is an empty set ? Thank you in advance 
June 5th, 2017, 07:00 AM  #2 
Member Joined: May 2017 From: Russia Posts: 34 Thanks: 5 
$\displaystyle (f(x^3)\sqrt{2})$ is a polynomial of degree 9. It has a root in $\displaystyle \mathbb{R}.$


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