Let $\displaystyle \alpha$ be any root the equation $\displaystyle x^5-x^3+x-2=0$. What will be the value of $\displaystyle [\alpha^6]$? Here $\displaystyle []$ means floor function.
No it is not. WolframAlpha says the real root is 1.20557 and hence the answer comes out to be 3.
But I want the procedure, not direct answer.
its more by guessing
substitute x=1 u get anegative value then substitute x=1.3 u get apositive value then according to cauchys theorem there is areal root between those two values of x meaning between x=1 and x=1.3 now take another two values of x between 1 and 1.3 and substitute again and so on