Classic olympiad problem · Algebra
Prove that a polynomial of degree n with real coefficients has at…
Prove that a polynomial of degree with real coefficients has at most real roots.
This is a proof problem. The answer is an argument, not a number. The solution is deliberately not posted here: reading a solution you didn't fight for teaches almost nothing. On Lemma you attempt it cold, take one of the 3 progressive hints only when genuinely stuck, then compare your proof against a full walkthrough and mark yourself with the same rubric a competition coordinator would use.
Train it on Lemma
This problem sits in the Olympiad Set: 89 proof problems (real IMO problems and the classics) with progressive hints, full walkthroughs and marking rubrics. 125 lessons, 1206 curated problems and unlimited generated practice at six difficulties. Free to start, no card, and every paid plan opens with 3 free days.
Find your levelMore Algebra problems
- IMO 1964, Problem 2IMO 1964, Problem 2 · difficulty 5/6
- Functional equationClassic (functional equation) · difficulty 4/6
- AM–GM: Prove that for positive reals a,b,c:…Classic (AM–GM) · difficulty 3/6
- All 89 problems →