find the value of........
Answers
Answer:
Required value of a is - 1 and b is - 9.
Step-by-step explanation:
It is given that ( x^2 + 1 ) is a factor of that given polynomial.
By using remainder theorem :
{ x - ( ± √1 ) }
By using remainder theorem : If ( x^2 + 1 ) is the factor of x^4 + x^3 + 8x^2 + ax + b = 0, then on changing x by ( ± 1 ) remainder will be 0.
Thus, when we take + 1 :
= > ( 1 )^4 + ( 1 )^3 + 8( 1 )^2 + a( 1 ) + b = 0
= > 1 + 1 + 8( 1 ) + a + b = 0
= > 2 + 8 + a + b = 0
= > 10 + a + b = 0
= > a = - b - 10 ... ( 1 )
Similarly, when we take - 1 :
= > ( - 1 )^4 + ( - 1 )^3 + 8( - 1 )^2 + a( - 1 ) + b = 0
= > 1 - 1 + 8( 1 ) - a + b = 0
= > 8 - a + b = 0
Substituting the value of a from ( 1 ) :
= > 8 - { - b - 10 } + b = 0
= > 8 + b + 10 + b = 0
= > 18 + 2b = 0
= > 2b = - 18
= > b = - 9
Therefore,
= > a = - b - 10
= > a = - ( - 9 ) - 10
= > a = 9 - 10
= > a = - 1
Hence the required value of a is - 1 and b is - 9.