Some conclusions on Roots of a Polynomial Equation

1. An equation of degree n has n roots, real or imaginary.
2. Surd and imaginary roots always occur in pairs, i.e. if 5-3i is a root of an equation, then 5 +3i is also its root. Similarly, if 3+SQRT(5) is a root of a given equation, then 3-SQRT(5) is also its root.
3. An odd degree equation has at least one real root, whose sign is opposite to that of its last term, provided that the coefficient of highest degree term is positive.
4. Every equation of an even degree whose constant term is negative and the coefficient of highest degree term is positive, has at least two real roots, one positive and one negative