Question

if{x+1} and {x-1} are the factors of px cube+x square-2x +q find values of p and q

Answer 1

Answer:

{x+1} and {x-1} are the factors of px^3+x ^ 2 - 2x +q

f ( x ) = px^3+x ^ 2 - 2x +q

f ( -1 ) = 0 and f ( 1 ) = 0

f ( -1 ) = p ( -1 ) ^ 3 + ( - 1 ) ^ 2 - 2 * -1 + q = 0

-p + 1 + 2 + q = 0

-p + 3 + q = 0

q - p = - 3 ------------------------1

f ( 1 ) = p ( 1 ) ^ 3 + (  1 ) ^ 2 - 2 * 1 + q = 0

p + 1 - 2 + q = 0

p - 1 + q = 0

p + q = 1 --------------------------2

p + q = 1

- p + q  = - 3   subtract  

-----------------------

2p  =  4

p = 4/ 2

   = 2

p + q = 1

q = 1 - p

  = 1 - 2

  = -1

therefore p = 2 and q = -1 ( answer )

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