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UPTET Feb 2014, q127

0. The polynomial P (x) = x4 - 2x3 + 3x2 - ax + 3a - 7 when divided by (x + 1) leaves the remainder 19. The value of a is

  • Option : C
  • Explanation : P (x) = (x + 1)· g (x) + 19,
    where g(x) is the quotient
    ⇒ P (x) - 19 = (x+l)· g (x)
    i.e. (x+l) divides P (x) - 19 completely.
    i.e. P (-1) - 19 = 0
    (-1)4 - 2(-1)3 + 3(-1)2 - a (-1) + 3a - 7 + 19 = 0
    1 + 2 + 3 + a + 3a - 7 -19 = 0
    ⇒ 4a = 20
    ⇒ a = 5.
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