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Math Help - Need help finding the x-intercepts

  1. #1
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    Need help finding the x-intercepts

    how do you find the x-intercepts if you have 0 = x^3 -9x^2 + 15x + 30
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  2. #2
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    I assume you mean "if you have y= x^3- 9x^2+ 15x+ 30" so the x-intercepts are where y= 0: x^3- 9x^2+ 15x+ 30= 0. Of course, you find them by solving that equation. I recommend crossing your fingers and hoping that there is at least one rational root. The rational root theorem tells us that if there is a rational root, it must be an integer that evenly divides the constant term, 30. The only possible rational roots are \pm 1, \pm 2, \pm 3, \pm 5, \pm 6, \pm 10, \pm 15, \pm 30. Try those and see if one or more satisfy the equation. If one does, you can divide by the corresponding factor to reduce to a quadratic equation.
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  3. #3
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    As it happens, this particular polynomial has no "nice" rational roots. To find the one real root, you'll have to use numerical methods.

    Note that y = -44 at x = -2, but y = 5 at x = -1. Then somewhere between x = -2 and x = -1, you must have y = 0.

    When x = -1.5, y = -16.125. So y = 0 must be between x = -1.5 and x = -1. Try, say, x = -1.25.

    And so forth, until you've got enough decimal places of accuracy.
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