Archive
27th of March 2017
Mathematics
Q:

If (x+1) and (x-1) are factors of ax3+ax2-2x+b,then find the values of a and b.Also find the third factor?

Nisha_vini29 - CBSE - Class IX

Monday, March 27, 2017 at 16:44:PM

A:

begin mathsize 16px style left parenthesis straight x plus 1 right parenthesis space and space left parenthesis straight x minus 1 right parenthesis space are space given space to space be space the space factors space of space ax cubed plus ax squared minus 2 straight x plus straight b
rightwards double arrow straight a left parenthesis 1 right parenthesis cubed plus straight a left parenthesis 1 right parenthesis squared minus 2 left parenthesis 1 right parenthesis plus straight b equals 0
rightwards double arrow straight a plus straight a plus negative 2 plus straight b equals 0
rightwards double arrow 2 straight a plus straight b equals 2
Also comma space straight a left parenthesis negative 1 right parenthesis cubed plus straight a left parenthesis negative 1 right parenthesis squared minus 2 left parenthesis negative 1 right parenthesis plus straight b equals 0
rightwards double arrow negative straight a plus straight a plus 2 plus straight b equals 0
rightwards double arrow straight b equals negative 2
So comma space 2 straight a minus 2 equals 2 rightwards double arrow 2 straight a equals 4 rightwards double arrow straight a equals 2

Thus comma space the space polynomial space is space 2 straight x cubed plus 2 straight x squared minus 2 straight x minus 2 rightwards double arrow straight x cubed plus straight x squared minus straight x minus 1
To space find space the space third space factor comma space divide space straight x cubed plus straight x squared minus straight x minus 1 space by space straight x squared minus 1. end style

Also, the doubt you posted on the 24th of March.

Here is your solution.

The coefficient of zx is -6 not -5. This makes it impossible to use the identity. This was why we took time to solve this. Hope this clears your doubt Nisha.

Monday, March 27, 2017 at 18:49:PM