Question

find the value of A and B so that (X + 1) and (x-1) are the factor of X^4 + ax^3 - 3x^2 + 2x

Answer 1

Hey friend !

I think the question should be :-

p(x) = x⁴ - ax³ -3x² + 2x + b

We have to find the values of "a" and "b"

Given :-

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

Hence ,
zeroes are = -1 and 1

p(1) = 1⁴ + a×1³ - 3×1² + 2× 1 + b
       = 1 + a - 3 + 2 + b = 0
       = a + b = 0                            --------> [1]

p(-1) = (-1)⁴ + a×-1³ - 3×-1² + 2× -1 + b
        = 1 - a - 3 -2 + b
       = -4 - a + b
        -a + b = 4                            --------> [2]

Adding equations 1 and 2 ,

2b =  4

b = 2

Put this value in p(x) :-

we get ,

a = -2

Answer 2

Answer:

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

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!!!