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I have 2 Questions:

  1. How to get the roots of the equation f (x) = 0 using Bolzano theorem? (f is a continuous function and we dont know its type(polynomial or else))
  2. How can the above algorithm be improved to count the number of double roots?
amz
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  • Give a reference to the theorem by Bolzano you are refering to. Besides, is $f$ continuous, is $f$ any function or a polynomial ? There is a place for improvement in the way your question is formulated, moreover without showing any personal work on the question – Jean Marie Apr 19 '21 at 11:38
  • I edited my question. f is continuous and we don't know its type. – amz Apr 19 '21 at 11:48
  • Reference here (It is only in some parts of the world where this result is known under the name "Bolzano's theorem") 2) The algorithm you are looking for must use a tuned version of Bisection method
    • – Jean Marie Apr 20 '21 at 23:13