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What substitution should be used to rewrite [tex]$4x^4 - 21x^2 + 20 = 0$[/tex] as a quadratic equation?

A. [tex]u = x^2[/tex]
B. [tex]u = 2x^2[/tex]
C. [tex]u = x^4[/tex]
D. [tex]u = 4x^4[/tex]

Answer :

We start with the equation
[tex]$$
4x^4 - 21x^2 + 20 = 0.
$$[/tex]

Notice that [tex]$x^4$[/tex] can be written as [tex]$(x^2)^2$[/tex]. This suggests that a substitution of the form
[tex]$$
u = x^2
$$[/tex]
will simplify the equation.

Substituting into the equation gives:
[tex]$$
4u^2 - 21u + 20 = 0.
$$[/tex]

This is now a quadratic equation in terms of [tex]$u$[/tex] and can be solved using standard methods such as factoring, completing the square, or the quadratic formula.

Thus, the appropriate substitution is:
[tex]$$
u = x^2.
$$[/tex]

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