How do we solve x 4

Bi-quadratic equation

We'll deal with the biquadratic equation in this article. We will explain to you what a biquadratic equation is and how to solve it. This article belongs to the field of mathematics.

In order to be able to understand this article well, some previous knowledge is unfortunately necessary. All those who do not yet know anything about the following topics, please read them briefly first. This knowledge is required in the following section:


Solve biquadratic equation

Before we start solving a bi-quadratic equation, you should first know what a bi-quadratic equation is. A biquadratic equation is an equation in the form: x4 + px2 + q = 0. A few examples for a better understanding:

  • x4 + 2x2 + 3 = 0
  • x4 + 5x2 + 2 = 0
  • x4 + 2x2 = 0

A little "trick" is used to solve these equations. We can then use the PQ formula through a so-called substitution. Substitution is generally understood to mean the replacement of one term by another. This is usually used to simplify the expression containing the term. For our biquadratic equation, this means that we have x2 = set z. Afterwards we can use the PQ formula as usual in order to then solve a quadratic equation. In the end we have to do a back substitution.

Example (explanation below):

For the starting equation we use the substitution z = x2 by. Then we apply the PQ formula and get two solutions (e.g.1 = 4 and z2 = 3). The substitution z = x2 now has to be undone.


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