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Math Help - problem regarding equation

  1. #1
    Senior Member Sambit's Avatar
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    Question problem regarding equation

    Let \alpha be any root the equation x^5-x^3+x-2=0. What will be the value of [\alpha^6]? Here [] means floor function.
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  2. #2
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    if it was a real root then the answer is 2
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  3. #3
    Senior Member Sambit's Avatar
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    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.
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  4. #4
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    Quote Originally Posted by Sambit View Post
    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
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