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
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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
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
harshi4221:
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