How can one verify the roots of a polynomial function?

Verifying the roots of a polynomial function can effectively be done by substituting the potential roots back into the original equation. When you substitute a value into the polynomial, if it is indeed a root, the result of this substitution should equal zero. This is based on the fundamental property of polynomial equations, where a root ( r ) satisfies the equation ( f(r) = 0 ).

For instance, if you have a polynomial ( f(x) ) and suspect that ( r ) is a root, calculating ( f(r) ) will confirm whether or not this is true. If ( f(r) = 0 ), it proves that ( r ) is a root of the polynomial.

Other methods mentioned, such as subtracting the roots from the original function, multiplying the roots together, or using the derivative, do not serve the purpose of directly confirming whether a specific value is a root. Substituting the roots back into the polynomial gives a direct verification of the accuracy of the roots found.