For what value(s) of p does the equation px+ (p - 1)x + (p - 1) = 0 have a repeated root?

Asked by Topperlearning User | 11th Sep, 2017, 10:19: AM

Expert Answer:

Given space equation space is space px squared plus left parenthesis straight p minus 1 right parenthesis straight x plus left parenthesis straight p minus 1 right parenthesis equals 0 space
straight a space equals space straight p comma space straight b equals straight p minus 1 comma space straight c equals straight p minus 1
For space repeated space root comma space straight D equals 0 space
therefore space straight b squared space minus space 4 ac equals 0 space
rightwards double arrow space left parenthesis straight p space minus space 1 right parenthesis squared space minus space 4 straight p left parenthesis straight p space minus space 1 right parenthesis space equals space 0 space
therefore space left parenthesis straight p space minus space 1 right parenthesis left parenthesis straight p space minus space 1 space minus space 4 straight p right parenthesis space equals space 0
space therefore space left parenthesis straight p space minus space 1 right parenthesis left parenthesis negative space 3 straight p space minus space 1 right parenthesis space equals space 0 space
therefore space straight p space minus space 1 equals space 0 space or space minus 3 straight p space minus space 1 space equals space 0
therefore space space straight p space equals space 1 space or space straight p space equals space minus 1 third

Answered by  | 11th Sep, 2017, 12:19: PM