= Interlacing roots of polynomials
{title2=$a_1\le b_1\le a_2\le\cdots\le a_d\le b_d$}
Two real <polynomials> with only real <roots of a polynomial> interlace when their ordered roots alternate, counting <multiplicity of a root>. For equal <polynomial degrees>, one ordering is the displayed chain; the opposite ordering is also permitted. Consecutive degrees give the analogous chain with one extra root at each end for the higher-degree <polynomial>. Strict interlacing uses strict inequalities. Weak interlacing permits common roots and follows as a <limit> of strict interlacing.
Back to article page
