B Roots of polynomials

Rishabh Narula

I was reading this book - " mathematical methods for physics and engineering"
in it in chapter 1 its says
"F(x) = A(x - α1)(x - α2) · · · (x - αr),"
this makes sense to me but then it also said

We next note that the condition f(αk) = 0 for k = 1, 2, . . . , r, could also be met
if (1.8) were replaced by
F(x) = A(x - α1)^m1(x - α2)^m2 · · · (x - αr)^mr

this confused me...how can you can you just raise each factor to powers m1,m2,...mr etc.How does the function still remain same?

HallsofIvy

Homework Helper
The function doesn't "remain the same" and this doesn't say it does. It just says that the two functions have the same zeros. Both $$(x- a_r)$$ and $$(x- a_r)^n$$ are 0 if and only if $$x= a_r$$.

"Roots of polynomials"

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