eli5 – What does root of an polynomial mean and what’s its importance?
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The roots of a polynomial are any values of the independent variable (typically x) that causes the value of the polynomial to be zero.
Example: y = x^2 has only one root, because only x=0 causes y=0.
Example: y=x^2 + 1 has no root because all real values of x cause y>0. (If you allow for imaginary numbers, it has 2 roots x=i and x=-i, where i = √-1).
Example: y=x^2 – 1 has two roots because x=1 and x=-1 both cause y=0.
This is important because methods of solving polynomials are easier if you’re solving for zero. For example, if you want to solve for what value of x yields some nonzero value of y, it is helpful to subtract that nonzero value from the polynomial before solving it.
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