what substitution should be used to rewrite $x^8 - 3x^4 + 2 = 0$ as a quadratic equation?

$u = x^2$
$u = x^4$
$u = x^8$
$u = x^{16}$

Question

what substitution should be used to rewrite $x^8 - 3x^4 + 2 = 0$ as a quadratic equation?

$u = x^2$
$u = x^4$
$u = x^8$
$u = x^{16}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Quadratic Form Equations" ], "new_concepts": [], "current_concepts": [ "Quadratic Form Equations", "Exponent Rules" ] } ## Identify the structure of the equation Using the *Quadratic Form Equations* knowledge point $$ \begin{aligned} &x^8 - 3x^4 + 2 = 0\ &(x^4)^2 - 3(x^4) + 2 = 0 \end{aligned} $$ ## Define the substitution variable Using the *Quadratic Form Equations* knowledge point $$ \begin{aligned} &u = x^4\ &u^2 - 3u + 2 = 0 \end{aligned} $$

(A) $u = x^2$

(B) $u = x^4$

(C) $u = x^8$

(D) $u = x^{16}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Form Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the structure of the equation

Define the substitution variable

Answer: