Question

find the value of A and b so that X + 1 and x minus 1 are factors of p (A) =X raise to power 4 + aX raise to power 3 minus 3 X raise to power 2 + 2 X + b​

Answer 1

Step-by-step explanation:

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