Question

find the values of 'a' and 'b' so that(x+1) and (x-1) are the factors of polynomial x^4+ax^3-3x^2+2x+b​

Answer 1

Case 1:

when(X+1) is factor of given equation:

X+1=0

X=-1

putting the value of X in equation:

=x^4+ax^3-3x^2+2x+b

=(-1)^4 +a(-1)^3-3(-1)^2 +2(-1) +b

=+1-a-3-2+b

=b-a-4......................(i)

Case 2:

(x-1)=0

X=1

putting the value:

=(1)^4+a(1)^3-3(1)^2+2(1)+b

=1+a-3+2+b

=a+b.................(ii)

by adding the equation (i) and (ii)

b-a-4

b+a

2b-4=0

2b=4

b=2

value of a=

a+b=0

a+2=0

a=-2