MathDB

Let

P(x)

be a polynomial with real coefficients. Let

\alpha_1 , \dots , \alpha_k

be the distinct real roots of

P(x)=0

. If

P'

is the derivative of

P

, show that for each

i=1,\dots , k

\lim_{x\to \alpha_i} \frac{(x-\alpha_i)P'(x)}{P(x)} = r_i,

for some positive integer

r_i

P5