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18 July, 08:37

3. Find all the zeroes of the polynomial x4 + 2x3 - 8x2 - 18x - 9, if two of its zeroes are 3

and - 3.

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Answers (2)
  1. 18 July, 08:45
    0
    x = 3, x = - 3, x = - 1 with multiplicity 2

    Step-by-step explanation:

    Given that x = 3 and x = - 3 are zeros then

    (x - 3) and (x + 3) are factors and

    (x - 3) (x + 3) = x² - 9 ← is a factor

    Using long division to divide the polynomial by x² - 9 gives

    quotient = x² + 2x + 1 = (x + 1) ² and equating to zero

    (x + 1) ² = 0 ⇒ x + 1 = 0 ⇒ x = - 1 with multiplicity 2

    Hence the zeros of the polynomial are

    x = 3, x = - 3, x = - 1 with multiplicity 2
  2. 18 July, 09:02
    0
    2b2t

    Step-by-step explanation:

    2b2t
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