eli5 – What does root of an polynomial mean and what’s its importance?

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eli5 – What does root of an polynomial mean and what’s its importance?

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Answer 1

Something the answers have not touched on is WHY they are important. Many equations are just roots of polynomials if you rearrange them.

3x = x² – 2

could be an equation we want to solve. It can be rewritten as

x² – 3x – 2 = 0

Now we can think of x² – 3x – 2 as our polynomial and the roots are the solution to our equation. The advantage is that if we know how to calculate the roots of a polynomial, we can solve many equations by looking at it from the perspective of roots of polynomials.