calc
posted by t on .
A basic fact of algebra states that c is a root of a polynomial f(x) if and only if f(x) = (xc)g(x) for some polynomial g(x). We say that c is a multiple root if f(x) = [(xc)^2](h(x)) where h(x) is a polynomial.
Show that c is a multiple root of f(x) if and only if c is a root of both f(x) and f'(x)

only if:
f(x) = (xc)^2 h(x)
f'(x) = 2(xc) h(x) + (xc)^2 * h'(x)
= (xc) * (2h + (xc)*h^2)
This should get you going. The "if" logic kind of works backwards from here.