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2 May, 15:56

The value 5 is an upper bound for the zeros of the function shown below. f (x) = x^4+x^3 - 11x^2-9x+18

A.) True

B.) False

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Answers (1)
  1. 2 May, 18:09
    0
    Answer: True

    Explanation:

    According to the rational zeros theorem, if x=a is a zero of the function f (x), then f (a) = 0.

    Given: f (x) = x⁴ + x³ - 11x² - 9x + 18

    From the calculator, obtain

    f (5) = 448

    f (4) = 126

    f (3) = 0

    f (2) = - 20

    f (1) = 0

    f (0) = 18

    f (-1) = 16

    f (-2) = 0

    f (-3) = 0

    The polynomial is of degree 4, so it has at most 4 real zeros.

    From the calculations, we found all 4 zeros as x = - 3, - 2, 1, and 3.

    Therefore

    f (x) = (x+3) (x+2) (x-1) (x-3).

    For x>3, f (x) increases rapidly. Therefore there are no zeros for x>3.

    The statement that x=5 is an upper bound for the zeros of f (x) is true.
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