A quartic is a polynomial of degree 4, meaning the highest exponent is 4.
Biquadratic can mean the same thing, but most mathematicians use the term biquadratic to refer to an equation of degree 4 with no odd powers. So for example we cannot have an x3 term. An example of a biquadratic is: x4 +x2 + 22=0
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Equations of the form z^4+az^2+a_0 are known as biquadratic equations. They are quartic equations. In general they can be solved by reducing them to a quadratic equation where x=z^2 is the variable. Then you can use the quadratic formula or factor. So plugging in x to the biquadratic giives us x^2+ax+a_0.
It is nothing more than a polynomial that is equivalent to another, but has fewer terms. For an example, see Wikipedia, under "quartic equation".
Each distinct real root is an x-intercept. So the answer is 4.
This would be a tesseract (a 4-dimensional hypercube) with a hypervolume of 16 quartic-inches. However, this is almost certainly not what you mean to ask. You need to reword your question.
(x - u)*(x - u)*(x + 2i)*(x - 2i) = (x2 - 2xu + u2)*(x2 + 4) = x4 - 2x3u + x2(u2 + 4) - 8xu + 4u2