Q25

Asked by sucharitasahoo1 | 26th Nov, 2017, 10:31: AM

Expert Answer:

begin mathsize 16px style dividend equals divisor cross times quotient plus remainder
dividend equals straight x to the power of 4 minus 6 straight x cubed plus 16 straight x squared minus 25 straight x plus 10
divisor equals straight x squared minus 2 straight x plus straight k
remainder equals left parenthesis straight x plus straight a right parenthesis
let space quotient space equals px squared plus qx plus straight r
straight x to the power of 4 minus 6 straight x cubed plus 16 straight x squared minus 25 straight x plus 10 equals open parentheses straight x squared minus 2 straight x plus straight k close parentheses open parentheses px squared plus qx plus straight r close parentheses plus left parenthesis straight x plus straight a right parenthesis
open space the space brackets
straight x to the power of 4 minus 6 straight x cubed plus 16 straight x squared minus 25 straight x plus 10 equals px to the power of 4 plus open parentheses straight q minus 2 straight p close parentheses straight x cubed plus open parentheses kp plus straight r minus 2 straight q close parentheses straight x squared plus straight x open parentheses qk minus 2 straight r plus 1 close parentheses plus open parentheses kr plus straight a close parentheses
comparing space coefficients
straight p equals 1....... left parenthesis 1 right parenthesis
straight q minus 2 straight p equals negative 6....... left parenthesis 2 right parenthesis
kp plus straight r minus 2 straight q equals 16....... left parenthesis 3 right parenthesis
qk minus 2 straight r plus 1 equals negative 25....... left parenthesis 4 right parenthesis
kr plus straight a equals 10....... left parenthesis 5 right parenthesis
from left parenthesis 1 right parenthesis space & space left parenthesis 2 right parenthesis space you space will space get space straight p space & space straight q space
then space find space straight r space using space straight p space and space straight q space in space left parenthesis 3 right parenthesis
then space straight k space from left parenthesis 4 right parenthesis space and space finally space straight a


end style

Answered by Arun | 27th Nov, 2017, 04:17: PM