Question

find the value of a and b so that (x+1) and (x-1) are factors of x⁴+ax³-3x²+2x+b​

Answer 1

As (x+1) and (x-1) are the factors of

$f(x) = {x}^{4} + a {x}^{3} - 3 {x}^{2} + 2x + b$

Then,

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

And, f(1) = 1 + a -3 + 2 + b = 0

So,

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

or, 2a -4 = 0

or, a = -2

Similarly, b = 2

Thus, a = -2 and b = 2

HOPE THIS COULD HELP!!!

Answer 2

Step-by-step explanation:

As (x+1) and (x-1) are the factors of

f(x) = {x}^{4} + a {x}^{3} - 3 {x}^{2} + 2x + bf(x)=x

4

+ax

3

−3x

2

+2x+b

Then,

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

And, f(1) = 1 + a -3 + 2 + b = 0

So,

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

or, 2a -4 = 0

or, a = -2

Similarly, b = 2

Thus, a = -2 and b = 2

HOPE THIS COULD HELP!!!