Minimize the number of roots

Algebra Level 5

Suppose \(p(x)\) and \(q(x)\) are polynomials of degree \(100\) with complex coefficients, having no common zeroes. Find the smallest possible total number of complex zeroes of the polynomials \(p,\) \(q,\) and \(p-q,\) counted without multiplicity.

Details and assumptions

When the zeroes are counted without multiplicity, the polynomial \(x^2(x-1)^3\) has two zeroes: \(x=0\) and \(x=1.\)

×

Problem Loading...

Note Loading...

Set Loading...