Polynomials (1 Viewer)

[kaz1]

Prove that if P(x) has root multiplicity m, then P'(x) has a root of multiplicity m-1


Thanks in advance.

 

[Timothy.Siu]

Prove that if P(x) has root multiplicity m, then P'(x) has a root of multiplicity m-1


Thanks in advance.

P(x)=(ax-b)^m . Q(x)
P'(x)=(ax-b)^m . Q'(x) +Q(x) . ma(ax-b)^(m-1)
P'(x)=(ax-b)^(m-1) ((ax-b)Q'(x)+Q(x))
which has multiplicity m-1

p.s. you could use (x-a)^m which should be easier.