CBSE Class 9 Answered

$If space both space left parenthesis straight x space minus space 2 right parenthesis space and space open parentheses straight x space minus space 1 half close parentheses space are space factors space of space px squared space plus space 5 straight x space plus space straight r comma space show space that space straight p space equals space straight r.$

Asked by Topperlearning User | 14 Sep, 2017, 01:30: PM

Expert Answer

$Let space straight f left parenthesis straight x right parenthesis space equals space px squared space plus space 5 straight x space plus space straight r Since space left parenthesis straight x space minus space 2 right parenthesis space is space straight a space factor space of space straight f left parenthesis straight x right parenthesis comma space we space have straight f left parenthesis 2 right parenthesis space equals space 0 rightwards double arrow straight p left parenthesis 2 right parenthesis squared space plus space 5 left parenthesis 2 right parenthesis space plus space straight r space equals space 0 rightwards double arrow 4 straight p space plus space 10 space plus space straight r space equals space 0 rightwards double arrow 4 straight p space plus space straight r space equals space minus 10 space space space space space space space space space.... left parenthesis 1 right parenthesis Also comma space open parentheses straight x space minus space 1 half close parentheses space is space straight a space factor space of space straight f left parenthesis straight x right parenthesis. rightwards double arrow straight f open parentheses 1 half close parentheses space equals space 0 rightwards double arrow straight p open parentheses 1 half close parentheses squared space plus space 5 open parentheses 1 half close parentheses space plus space straight r space equals space 0 rightwards double arrow straight p over 4 space plus space 5 over 2 space plus space straight r space equals space 0 rightwards double arrow straight p space plus space 10 space plus space 4 straight r space equals space 0 rightwards double arrow straight p space plus space 4 straight r space equals space minus 10 space space space space space space space.... left parenthesis 2 right parenthesis From space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis comma space we space have 4 straight p space plus space straight r space equals space straight p space plus space 4 straight r rightwards double arrow 3 straight p space equals space 3 straight r rightwards double arrow straight p space equals space straight r$