A nice problem by Nikolai Nikolov

Algebra Level 3

How many ordered pairs ( a , b ) (a,b) are there such that :

a , b ∈ C , a ≠ 0 a,b \in \mathbb{C},a≠0 , and for every root ω k ( k = 1 , 2 , 3 , 4 ) \omega_{k}(k=1,2,3,4) of the equation z 4 − a z 3 − b z − 1 = 0 z^{4}-az^{3}-bz-1=0 holds the inequality ∣ a − ω k ∣ ≥ ∣ ω k ∣ |a-\omega _{k}|\ge|\omega _{k}| ?

Infinitely many 0 2 4

Haosen Chen by Haosen Chen , 20, China

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

0 solutions

No explanations have been posted yet. Check back later!

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...