Question

For what value of a and b, the polynomial x^4+ax^3+2x^2-3x+b is exactly divisible by (x-1) and (x+1)

Answer 1

Answer:

X=-1 and x=2

X^4+ax^3–3x^2+2x+b=0

Put x=-1

(-1)^4+a(-1)^3–3(-1)^2+2(-1)+b=0

1-a-3–2+b=0

-a+b-4 =0

-a+b=4=>(1)

Putx=2

16+8a-12+4+b=0

8a+b=-8=>(2)

equ.(1)-(2)

-9a=12

a =-4/3

Put equ.1 in a= -4/3

-(-4/3)+b=4

4/3+b=4

b=8/3