英语词汇“root”的翻译、意思、用法、释义-英汉经管词典

单词

root

释义

root

of an equation

A value of the argument of an equation which causes the equation to be satisfied. For example, if 2x - 4 = 0, x = 2 is a root (in this case the only root) of the equation. The equation y² - 7y + 10 = 0 has two real roots, y = 2 and y = 5. A given equation may or may not have any real roots, and it may have one or many. In a few cases, the form of an equation tells us how many real roots there will be and allows us to locate them quite easily. In the linear equation ax + b = 0, where a ≠ 0, there is always one real root, x = -b/a. If ay² + by + c = 0, where a ≠ 0, there may be two real roots, possibly equal, or none. The roots are given by 0198607679.root-of-an-equation.1.jpg If b² > 4ac there are two distinct real roots; if b² = 4ac there are two equal real roots, and if b² < 4ac there are no real roots. For most types of equation there are no comparably simple rules; the existence and location of roots have to be checked by numerical methods.

See also:

unit root

of a number

The number, x, whose rth power equals y. If y = x^r, x is the rth root of y. For example, if y = x², x is the square root of y, written x = √y = y^1/2 ; if z = x³, x is the cube root of z, written 0198607679.root-of-a-number.1.jpg . The number and sign of real roots depends on whether r is even or odd. If r is even, that is divisible by 2, if y > 0 it has at least two real roots; if x^r = y then (-x)^r = y also, because (-x)^r = (-1)^r (x)^r = x^r = y. If y < 0 and r is even, y has no real rth roots; all rth roots of y are imaginary numbers involving i = 0198607679.root-of-a-number.2.jpg . If r is odd, y always has only one real rth root, which must have the same sign as y, because all odd powers of -1 equal -1.

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