if hcf of (x-5) (x squared-x-a) and (x-4)(x squared-2x-b) is (x-5)(x-4). find the values of a and b respectively

Asked by aa610030 | 24th Nov, 2015, 07:09: PM

Expert Answer:

begin mathsize 14px style L e t space p left parenthesis x right parenthesis equals left parenthesis x minus 5 right parenthesis left parenthesis x squared minus x minus a right parenthesis space a n d space q left parenthesis x right parenthesis equals left parenthesis x minus 4 right parenthesis left parenthesis x squared minus 2 x minus b right parenthesis S i n c e space left parenthesis x minus 4 right parenthesis left parenthesis x minus 5 right parenthesis space i s space t h e space h c f space o f space p left parenthesis x right parenthesis space a n d space q left parenthesis x right parenthesis comma space left parenthesis x minus 4 right parenthesis space a n d space left parenthesis x minus 5 right parenthesis space a r e space t h e space f a c t o r s space o f space p left parenthesis x right parenthesis space a n d space q left parenthesis x right parenthesis. rightwards double arrow p left parenthesis 4 right parenthesis equals 0 space a n d space q left parenthesis 5 right parenthesis equals 0 rightwards double arrow left parenthesis 4 minus 5 right parenthesis left parenthesis 16 minus 4 minus a right parenthesis equals 0 space a n d space left parenthesis 5 minus 4 right parenthesis left parenthesis 25 minus 10 minus b right parenthesis equals 0 rightwards double arrow negative 1 left parenthesis 12 minus a right parenthesis equals 0 space a n d space 1 left parenthesis 15 minus b right parenthesis equals 0 rightwards double arrow negative 12 plus a equals 0 space a n d space 15 minus b equals 0 rightwards double arrow a equals 12 space a n d space b equals 15 end style

Answered by Rashmi Khot | 25th Nov, 2015, 08:36: AM