[is3zzz]

Consider the following quadratic equation:  x² + bx +42.392 = 0.
If one of the roots is 17.706, what is the value of b?
Error tolerance:  ±0.001
 
What does it mean by root is 17.706?

[AWK]

(x-x₁)(x-x₂)=x²+(x₁+x₂)x+x₁x₂=0
x₁ and x₂ are roots of this equation

[Yggdrasil]

The roots of the equation are the zeroes.  In other words, r is a root of f(x) if f(r) = 0.

[AWK]

The roots of the equation are the zeroes.  In other words, r is a root of f(x) if f(r) = 0.

[Yggdrasil]

http://en.wikipedia.org/wiki/Zero_of_a_function

[AWK]

Zero of a function is not a root of equation

[Yggdrasil]

In the example you gave, x₁ and x₂ are zeros of the function.  By zero, I mean the values of x at which f(x) = 0.  What definition of "zero of a function" are you using?

[Borek]

I feel like it is a wording problem - and I am with AWK on this one. Root refers to the function argument, zero of the function refers to the function value. You are carelessly mixing both things. Root of an equation is such a value of argument for which function value is zero.

[Yggdrasil]

It's probably more of a regional difference.  In America, I've always heard of the zero of a function refer to the value of the argument for which the value of the function is zero (see the wikipedia article, it too describes zero and root as synonymous; for a more definitive source see http://mathworld.wolfram.com/Root.html).

[AWK]

Mathword says:
The roots (sometimes also called "zeros") of an equation
are the values of  for which the equation is satisfied.

Note "zeros" and sometimes  all in () - for me it means it is local or incorect naming