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Roots & Solutions

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
Graph of f(x) = x2 + 2x − 3