The number of real roots of $$ \frac{3}{x-3}+\frac{5}{x-5}+\frac{17}{x-17}+\frac{19}{x-19} = x^2 -11x -4 $$ How to solve without actually finding the roots or is it the only way? I know that if the equation changes it's sign between two no.s it will have at least one root contained in them.
2026-04-22 01:46:16.1776822376
6th degree equation
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Hint: Use descartes rule of sign after you make the expression in the general form of a polynomial. see:https://en.wikipedia.org/wiki/Descartes%27_rule_of_signs.