A polynomial equation has the form a0xn + a1xn-1 + a 2xn-2 + ... + an-2x2 + an-1x + an = 0in which the coefficients a0, a1, ..., an are constants, the leading coefficient a0 is not equal to zero, and n is a positive integer. The greatest exponent n is the degree of the equation. Equations of the first, second, third, fourth, and fifth degrees are often called, respectively, linear, quadratic, cubic, biquadratic or quartic, and quintic equations. Other important types of equations are algebraic, as in = = 7; trigonometric, as in sin x + cos 2x = y; logarithmic, as in log x + 2 log (x + 1) = 8; and exponential, as in 3x + 2x - 5 = 0. Diophantine equations are equations in one or more unknowns, usually with integral coefficients, for which integral solutions are sought. Differential and integral equations, which involve derivatives or differentials, and integrals, occur in calculus and its applications.
