To rewrite the equation [tex]\(4x^4 - 21x^2 + 20 = 0\)[/tex] as a quadratic equation, we can use a suitable substitution. Let's analyze the given equation step by step.
1. Notice the term [tex]\(4x^4\)[/tex] and [tex]\( -21x^2\)[/tex] in the equation. With the goal of rewriting it into a quadratic form, we can make a substitution.
2. One effective substitution for simplifying such expressions is to let a new variable [tex]\(u\)[/tex] represent [tex]\(x^2\)[/tex]. By doing this:
[tex]\[
u = x^2
\][/tex]
3. Plugging [tex]\(u = x^2\)[/tex] into the original equation, we obtain:
[tex]\[
4(x^2)^2 - 21(x^2) + 20 = 0
\][/tex]
4. Simplify this substitution:
[tex]\[
4u^2 - 21u + 20 = 0
\][/tex]
Now, the equation [tex]\(4u^2 - 21u + 20 = 0\)[/tex] is a quadratic equation in [tex]\(u\)[/tex].
Thus, the correct substitution you should use is:
[tex]\[
u = x^2
\][/tex]
