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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- Jul 9th 2012, 07:59 AMkmerr98277Find 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. - Jul 9th 2012, 08:04 AMrichard1234Re: 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 $\displaystyle 0 = x^4 - 10x^2 - 96$. Quartics are not easy to solve but you can let $\displaystyle z = x^2$, so

$\displaystyle 0 = z^2 - 10z - 96$. This factors to $\displaystyle 0 = (z-16)(z+6) \Rightarrow z = x^2 = 16, -6 \Rightarrow x = \pm 4, \pm \sqrt{6}i$. Discard the imaginary solutions since the x-axis only takes on real values. Therefore the x-intercepts are (-4,0) and (4,0). - Jul 9th 2012, 08:26 AMkmerr98277Re: Find the intercepts of y=x^4-10x^2-96
Thanks!