Question

find the value of p and q so that x-1 and x+1 are factor of x^4+px^3+2x^2-3x+q

Answer 1

x-1 and x+1 are factors of x⁴+px³+2x²-3x+q

x-1 = 0 ; x = 1

x+1 = 0 ; x = -1

Put x = ±1 to know the values of p and q

Put x = 1

(1)⁴+p(1)³+2(1)²-3(1)+q = 0

1+p+2-3+q = 0

p+q+3-3 = 0

p+q = 0 -------(1)

Put x = -1,

(-1)⁴+p(-1)³+2(-1)²-3(-1)+q = 0

1-p+2+3+q = 0

-p+q+3+3 = 0

-p+q = -6 ------(2)

(1) + (2)

p + q = 0
-p + q = -6
---------------
2q = -6

q = -6/2

q = -3

p+q = 0

p+(-3) = 0

p = 3

Therefore, p = 3 and q = -3

Hope it helps

Answer 2

Answer:

Step-by-step explanation: