Archive
22nd of March 2017
Mathematics
Q:

If x2 - 3x + 2 is a factor of the polynomial x4 - ax3 + b then find the values of a and b?

Vikas Mahajan - CBSE - Class IX

Wednesday, March 22, 2017 at 17:46:PM

A:

begin mathsize 16px style straight x squared space minus space 3 straight x space plus space 2 space equals space left parenthesis straight x space minus space 2 right parenthesis left parenthesis straight x space minus space 1 right parenthesis space space
Given space that space straight x squared space minus space 3 straight x space plus space 2 space is space straight a space factor space of space straight x to the power of 4 minus ax cubed plus straight b
that space means comma space left parenthesis straight x space minus space 2 right parenthesis left parenthesis straight x space minus space 1 right parenthesis space is space straight a space factor space of space straight x to the power of 4 minus ax cubed plus straight b
When space straight x space equals space 1 comma space space
1 to the power of 4 space minus space straight a left parenthesis 1 right parenthesis cubed space plus space straight b space equals space 0 space space
rightwards double arrow negative straight a space plus space straight b space equals space minus 1 space.... left parenthesis straight i right parenthesis space space
When space straight x space equals space 2 comma space space
2 to the power of 4 space minus space straight a left parenthesis 2 right parenthesis cubed space plus space straight b space equals space 0 space space
rightwards double arrow 16 space minus space 8 straight a space plus space straight b space equals space 0 space space
rightwards double arrow negative 8 straight a space plus space straight b space equals space minus 16 space space space space..... left parenthesis ii right parenthesis

On space solving space the space equations space left parenthesis straight i right parenthesis and space left parenthesis ii right parenthesis comma space we space get
straight a space equals fraction numerator space 15 over denominator 7 end fraction comma space straight b space equals space 8 over 7 end style

Wednesday, March 22, 2017 at 18:03:PM