which equation has two roots?

$x^2 - 12x + 20 = 0$

$x + 8 = 0$

$x^3 - 12x + 20 = 0$

all of the choices

Question

which equation has two roots?

$x^2 - 12x + 20 = 0$

$x + 8 = 0$

$x^3 - 12x + 20 = 0$

all of the choices

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 Equations", "Degree of Polynomial", "Fundamental Theorem of Algebra" ], "new_concepts": [], "current_concepts": [ "Quadratic Equations", "Degree of Polynomial", "Fundamental Theorem of Algebra", "Polynomial Roots" ] } ## Analyze the degree of each polynomial equation Using the *Degree of Polynomial* and *Fundamental Theorem of Algebra* knowledge points $$ \begin{aligned} &\text{Degree of } x^2 - 12x + 20 = 0 \text{ is } 2 \implies 2 \text{ complex roots}\ &\text{Degree of } x + 8 = 0 \text{ is } 1 \implies 1 \text{ root}\ &\text{Degree of } x^3 - 12x + 20 = 0 \text{ is } 3 \implies 3 \text{ complex roots} \end{aligned} $$ ## Determine the number of real roots for the quadratic equation Using the *Quadratic Equations* knowledge point $$ \begin{aligned} &x^2 - 12x + 20 = 0\ &(x - 10)(x - 2) = 0\ &x = 10 \quad \text{or} \quad x = 2 \end{aligned} $$

(A) $x^2 - 12x + 20 = 0$

(B) $x + 8 = 0$

(C) $x^3 - 12x + 20 = 0$

(D) All of the choices

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

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QUESTION IMAGE

Question

Explanation:

Analyze the degree of each polynomial equation

Determine the number of real roots for the quadratic equation

Answer: