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) = x^{2} +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: