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15 November, 23:16

The function f (x) = x ^3 + 2x^2 - 5 x - 6 has a root at 2. Name all roots of this function.

a.-2, - 1, - 3

b. 2, 1, 3

c. 2, - 1, - 3

d.-2, 1, 3

+3
Answers (1)
  1. 15 November, 23:49
    0
    sub x=1 into f (x),

    remainder = 1^3+2 (1) ^2-5 (1) - 6 = - 8

    since remainder≠0, x=1 is not a root of the function

    sub x=-1,

    remainder = (-1) ^3+2 (-1) ^2-5 (-1) - 6 = 0

    by remainder theorem,

    x=-1 is a root of f (x)

    hence, the correct ans is c
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