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单词 polynomial
释义 polynomial

A function of the form y = f(x), defined in terms of a sum of terms each of which is a coefficient times a power of x. A linear function is a first-order polynomial, such as y = ax + b. A quadratic is a second-order polynomial, such as y = ax2 + bx + c. A cubic is a third-order polynomial, such as y = ax3 + bx2 + cx + d. In all cases it is assumed that a € 0, though any of the remaining coefficients may be zero. An Nth order polynomial takes the form y = aN xN + aN - 1 xN - 1 + … + a0. An Nth order polynomial can be shown to have N roots, that is N values of x for which y = 0. These roots may be real, imaginary or complex numbers. If the N roots are known, y can be factorized, that is, written as y = aN (x - r1) (x - r2 ) … (x - rN ). Linear and quadratic polynomial equations can be solved analytically by simple formulae. The cubic can in principle be solved analytically, but the procedure is so complicated that numerical methods are normally used instead. For quartics and above numerical methods have to be used to find the roots of polynomial equations.

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更新时间:2025/1/22 19:47:05