Coefficient

Coefficient, the numerical or literal factor prefixed to an unknown quantity in any algebraic term. Thus in the expression $ax\; -\; 2by^3\; +\; \backslash sqrt\{3\}x^2\; -\; (a\; +\; 5)y$ there are four terms, and the coefficients are, in order, $a$, $2b$, $\backslash sqrt\{3\}$, and $(a\; +\; 5)$. A special and very important instance is found in the phrase Differential Coefficient (q.v.) of a given function with reference to one or more of the variables involved. In the theory of equations, also, coefficients play an important part: thus, in the cubic $x^3\; +\; ax^2\; +\; bx\; +\; c\; =\; 0$, we know that (supposing the 3 roots are $p$, $q$, $r$) $p\; +\; q\; +\; r\; =\; -a$, $pq\; +\; qr\; +\; rp\; =\; b$, and $pqr\; =\; -c$.