Question

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

Answer 1

a.(x+1)
x+1=0
x=-1
x⁴+ax³-3x²+2x+b
(-1)⁴+a(-1)³-3(-1)²+2(-1)+b
1-a-3-2+b
-4-a+b=o
b-a=4

Answer 2

Heya!!

-------------------------

If x+1 and x-1 are factors of p(x) = x^4+ ax^3 -3x^2 + 2x + b..

Then p(-1)=p(1)= 0

=) (-1)^4 + a(-1)^3 -3(-1)^2 +2(-1)+b = 0

=) 1 -a -3 -2 + b = 0

=) b-a = 4.

And

=) (1)^4 +a(1)^3 -3(1)^2+2(1) +b = 0

=) 1 + a- 3+2+b = 0

=) a+b = 0

Means two equations r:

b-a = 4
a+b= 0

Add both equations,

=) 2b = 4

=) b= 4/2 = 2

Solve for a = -2

Hope it helps u :)