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Math Help - Find the intercepts of y=x^4-10x^2-96

  1. #1
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    Find the intercepts of y=x^4-10x^2-96

    Find the intercepts of y=x^4-10x^2-96
    I can't seem to find them. I set y to zero to find x and set x to zero to find y. Thanks.
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  2. #2
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    Re: Find the intercepts of y=x^4-10x^2-96

    When x = 0, y = -96, so the y-intercept is (0,-96).

    When y = 0, you have the quartic equation 0 = x^4 - 10x^2 - 96. Quartics are not easy to solve but you can let z = x^2, so

    0 = z^2 - 10z - 96. This factors to 0 = (z-16)(z+6) \Rightarrow z = x^2 = 16, -6 \Rightarrow x = \pm 4, \pm \sqrt{6}i. Discard the imaginary solutions since the x-axis only takes on real values. Therefore the x-intercepts are (-4,0) and (4,0).
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    Re: Find the intercepts of y=x^4-10x^2-96

    Thanks!
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