Wednesday 29 March 2017

Polynomial roots of degree 2



Since every polynomial of degree 'n' has 'n' complex roots.



Then what about $P(x)=x^2$ .




Isn't $x=0$ the only possible root of this polynomial ?


Answer



A polynomial of degree $n$ has $n$ roots counting multiplicity. That means that if we have a factor $$(x - a)^k$$



we count the root $a$ a total of $k$ times, once per linear factor. In particular, $x^2$ has a root at $0$ of multiplicity $2$.


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