math

Find all zeros of the function f(x)=16x^3-48x^2-145x-75
Please help ASAP!!! :(

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asked by Andrea
  1. Start with factor of -75
    f(x)=16x^3-48x^2-145x-75
    f(1) = 16 - 48 - 145 - 75 ≠ 0
    f(-1) = -16 - 48 + 145 - 75 ≠0
    f(3) ≠ 0
    f(-3) ≠ 0
    f(5) = 0 , yeah!!! , so x-5 is a factor
    using synthetic division by x-5
    we have 16x^3-48x^2-145x-75 = (x-5)(16x^2 + 32x - 15)

    so you have x = 5 and the two roots of 16x^2 + 32x - 15 = 0

    I will leave it up to you to find those two roots, let me know what you get.
    hint: they are rational.

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    posted by Reiny
  2. I got -3/4 and -5/4

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    posted by Andrea
  3. Good job. You found Reiny's typo.

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