eli5 – What does root of an polynomial mean and what’s its importance?
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Let’s define a polynomial as a function f(x) = ax² + bx + c
Of course, you could have x³ or x^4 or other terms in there as well, but we’ll use a quadratic for simplicity.
The roots of a polynomial are the values of x such that f(x) = 0
For example the easiest one, f(x) = x², only has one root – x = 0. When x = 0, f(x) = 0 because (0)² = 0.
The importance of the roots depends on the kind of problem you are trying to solve, but in general it tells you where the function goes from positive to negative (in cases where it has multiple roots,) or that the function is only ever positive or negative (in cases where it either has no roots, or only has one root)
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