Quartic roots inequality complex coefficients

2425MasterPolynomialsComplex Numbers

Spring Mathematical Competition

Find all complex numbers $a \neq 0$ and $b$ such that for every complex root $w$ of the equation $z^{4}-a z^{3}-b z-1=0$ the inequality $|a-w| \geq|w|$ holds.

0 students attempted0% solvedRating 2425

Related practice paths

Olympiad-Style PracticeDeep contest practice for proof-style problem solving.How to Qualify for AIMEScore goals, contest choice, and prep habits for AIME hopefuls.How to Review Missed AMC ProblemsTurn missed problems into a repeatable improvement loop.

Ready to check your answer?

Create an account to submit answers, save history, and track your rating.

Progressive Hints

Unlock hints one at a time — each reveals a little more without spoiling the solution.

Step-by-Step Solutions1

Multiple solution approaches with detailed walkthroughs, unlocked after you solve the problem.

AI-Powered Grading

Instant feedback on your answer — handles fractions, decimals, and equivalent forms.

Curated problem bank

Supported tracks for AMC, AIME, MATHCOUNTS, and olympiad-style training, plus global problem sources like UKMT, Euclid, and Kangaroo.

Quartic roots inequality complex coefficients

2425MasterPolynomialsComplex Numbers

Spring Mathematical Competition

Find all complex numbers $a \neq 0$ and $b$ such that for every complex root $w$ of the equation $z^{4}-a z^{3}-b z-1=0$ the inequality $|a-w| \geq|w|$ holds.

0 students attempted0% solvedRating 2425