for what value

comparing with the standard quadratic eqn we get,

a=p+1

b=-3(p-1)

c=-(p-1)

for the roots to be real and equal,

 we must have the value of the discriminant equal to zero.

so

[9(p-1)(p-1)]+4[(p+1)(p-1)]=0

(p-1){ [9(p-1)]+4(p+1)]=0

(p-1)[13p-5]=0

so

p=1

or

p=5/13

p=13/5