Answer:
It is important to consider multiplicity of root in factorization of polynomial equations.
Explanation:
We define multiplicity as:
- The multiplicity of a root of a polynomial equation is the number of times it appears in the solution.
- For example, the number of times a given polynomial equation has a root at a given point is the multiplicity of that root.
- Thus, if we do not consider the multiplicity of a root we may consider the discrete root only and not the number of times the root repeats itself and end up calculating wrong roots for the polynomial equation.
- Multiplicity tells us that how many times does a factor repeats itself in the factorization of a polynomial.
- If r is a zero of a polynomial and it repeats itself k times in the factorization then we say that r has multiplicity k.
- Zeroes with a multiplicity of 1 are often called simple zeroes.
Thus, it is important to consider multiplicity of root in factorization of polynomial equations.