The roots of a polynomial always come in complex conjugate pairs. Therefore there are zero, two or four real roots. Assume the general case that the roots are a+bi and c+di. The product of all the roots must equal 1. Therefore 1 = a^2 + b^2 +c^2 +d^2. All real numbers have a square>=0, therefore at least one of the terms a,b,c or d must be imaginary, and therefore at least 2 must be imaginary. Therefore there can be a maximum of only 2 real roots.

Posted by Kenny M
on 20110802 17:48:55 