if p{x} = x^4 – 2x^3 + 3x^2 – ax – b when divided by x – 1 , the remainder is 6 . then find the value of a + b.

1 thought on “if p{x} = x^4 – 2x^3 + 3x^2 – ax – b when divided by x – 1 , the remainder is 6 . then find the value of a + b.”

1. Answer:

   There is theorem known as “Polynomial Remainder Theorem” or “ Bezout’s Theorem”. It is Stated as –

   A Polynomial f(x) if divided by a linear polynomial (x-a) leaves remainder which equals f(a).

   So , getting back to our question –

   f(x) = x^4 – 2x^3 + 3x^2 – ax + b

   So , when it is divided by (x – 1) it’ll leave a remainder = f(1) = 5 (Given).

   f(1) = 1^4 – 2×1^3 + 3×1^2 – a×1 + b = 5

   => 1 – 2 + 3 – a + b = 5

   => a – b = (-3) …. Eqn(1)

   Now , Similarly –

   f(-1) = (-1)^4 – 2×(-1)^3 + 3×(-1)^2 – a×(-1) + b = 19

   => 1 + 2 + 3 + a + b = 19

   => a + b = 13 …. Eqn(2)

   Now , adding equations (1) and (2) , We’ll get –

   (a+b) + (a-b) = (-3) + 13

   => 2a = 10 => a = 5

   So , (a +b) = 13 implies b = 8

   Hence , Values of a and b are 5 and 8 respectively.

   Plz mark as brainlist..

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