What is the deal with roots solutions?
The solution of a polynomial equation, f(x), is the point whose root, r, is the value of x when f(x) = 0. Confusing semantics that are best clarified with a few simple examples.
| Equation | Solution | Root |
|---|---|---|
| f(x) = 3x + 1 | ($$\frac{-1}{3}$$, 0 ) since that is the point at which f(x) is zero. | $$\frac{-1}{3}$$ because it is the value of x for which f(x) = 0. |
| f(x) = x2 +2x − 3 |
(-3, 0) and (1, 0) are the solutions to this equation since -3 and 1 are the values for which f(x) = 0.
See picture below. |
-3 and 1 are the roots. |
