How to find all the real roots of

Mara Cook

Mara Cook

Answered question

2022-06-21

How to find all the real roots of x 9 2021 x 3 + 2020

Answer & Explanation

humbast2

humbast2

Beginner2022-06-22Added 21 answers

A related substitution to use would be x 3 = 2020 y which yields
2020 y 3 2021 y + 1 = 0
Clearly y = 1 is a root of this equation by rational root theorem, so we can factor this into
( y 1 ) ( 2020 y 2 + 2020 y 1 ) = 0
by polynomial long division. Quadratic equation gives the last two solutions in y to be
y = 1 2 ± ( 1 2 ) 2 + 1 2020 = 1 2 ± 1 2 506 505

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