Page "Polynomial" Paragraph 34

0 is the polynomial equation corresponding to P. The solutions of this equation are called the roots of the polynomial ; they are the zeroes of the function ƒ ( corresponding to the points where the graph of ƒ meets the x-axis ).

A number a is a root of P if and only if the polynomial x − a ( of degree one in x ) divides P. It may happen that x − a divides P more than once: if ( x − a )< sup > 2 </ sup > divides P then a is called a multiple root of P, and otherwise a is called a simple root of P. If P is a nonzero polynomial, there is a highest power m such that ( x − a )< sup > m </ sup > divides P, which is called the multiplicity of the root a in P. When P is the zero polynomial, the corresponding polynomial equation is trivial, and this case is usually excluded when considering roots: with the above definitions every number would be a root of the zero polynomial, with undefined ( or infinite ) multiplicity.

With this exception made, the number of roots of P, even counted with their respective multiplicities, cannot exceed the degree of P.