4 мая 2019 г. · The best way to solve this is to use Sturm's theorem. This gives an algorithm for computing the number of distinct real roots of any polynomial.

7 мар. 2021 г. · The total number of real roots of the polynomial of degree n is X. Hence, if X=n, all the roots of the polynomial are real.

26 июл. 2015 г. · For the specific polynomial you've given, we can write it as x(x−1)(x6+1)+15=0. So any real root x must satisfy x(x− ...

20 февр. 2013 г. · If you need to find all of the roots of an arbitrary polynomial, the Jenkins-Traub algorithm is easily the best, both in terms of efficiency and robustness.

10 янв. 2013 г. · Using Descartes' rule of signs, we count the number of sign changes. There are two so there are either two positive root or no positive roots.

29 окт. 2015 г. · Using Descartes Rule we get the possibilities of only 2 real roots or none. And since f(0)<0 and f(∞)=f(−∞)=∞ so 2 real roots are confirmed.

4 мая 2016 г. · You can use Cartesian rule of signs to get an upper bound on the number of real roots. An even stronger method is to use Sturm's theorem to get ...

27 сент. 2017 г. · To count the real roots: Look at the derivative, is it always positive? Could you have two real roots if the derivative is always positive? – ...

5 февр. 2023 г. · I'm creating a program to find the real roots of any given polynomial. It takes a user given polynomial as input and tries to find its roots.

1 нояб. 2017 г. · The derivative is 15x4−30x2−120=15(x2−4)(x2+2). So there are only two turning points, at x=±2, and so at most three real roots.