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Derivative and Root Multiplicity
If $$x=a$$ is a root of multiplicity $$m$$ of $$f(x)$$, then:
$$f(a)=f'(a)=\cdots=f^{(m-1)}(a)=0$$
while:
$$f^{(m)}(a)\neq0$$
Usage
- Used to determine the multiplicity of a polynomial root using derivatives.
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Derivative and Root Multiplicity
If $$x=a$$ is a root of multiplicity $$m$$ of $$f(x)$$, then:
$$f(a)=f'(a)=\cdots=f^{(m-1)}(a)=0$$
while:
$$f^{(m)}(a)\neq0$$
Usage
- Used to determine the multiplicity of a polynomial root using derivatives.
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