What is value of x if x^4 - x^2= infinity?

Answer 1

This may be factored to (x^2 - x)(x^2 + x). or, to further factor: x(x - 1)x(x + 1).

From Quora see this answer that it is not possible for a quadratic equation to equal zero:

Okay, all that is preliminary to your question. Your question is, when are the solutions to a quadratic equation infinity. Well, let’s think about what that means. First of all, it is clear that it is not possible to have one solution at infinity but the other solution finite. If that were the case, we would have some finite number times infinity, which cannot equal zero.

So the question is, is it possible for both solutions to be infinity? What would this look like?

In the quadratic formula, the only way to make it infinity would be if a = 0. Then the denominator would be zero, and hence the whole equation would be “infinity.” But if a = 0, then the equation is no longer quadratic, it is linear, right? For example,  is the same as . That is just a line, it is linear, not quadratic. But every line crosses the x-axis somewhere, right? The only time it does not is when it is parallel to the x-axis. That is, when it has a slope of 0. That means that b = 0. So now we have . In other words, 0 = c. But then c = 0.

In other words, there is no such equation. As the other answer said, all quadratic equations cross the x-axis at a finite point. (Notice that those points are not necessarily real! If  is negative, then the equation actually has imaginary roots. But they are still finite.)