which system of equations can you use to find the roots of the equation?
(x^3 - 10x = x^2 - 6)

$\begin{aligned} y &= x^3 - x^2 + 10x + 6 \\ y &= 0 \end{aligned}$

$\begin{aligned} y &= x^3 - x^2 + 10x \\ y &= 6 \end{aligned}$

$\begin{aligned} y &= x^3 - 10x \\ y &= x^2 - 6 \end{aligned}$

Question

which system of equations can you use to find the roots of the equation?
(x^3 - 10x = x^2 - 6)

$\begin{aligned} y &= x^3 - x^2 + 10x + 6 \\ y &= 0 \end{aligned}$

$\begin{aligned} y &= x^3 - x^2 + 10x \\ y &= 6 \end{aligned}$

$\begin{aligned} y &= x^3 - 10x \\ y &= x^2 - 6 \end{aligned}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Equations Graphically", "Systems of Non-linear Equations" ], "new_concepts": [], "current_concepts": [ "Solving Equations Graphically", "Systems of Non-linear Equations" ] } ## Identify the given equation $$ x^3 - 10x = x^2 - 6 $$ ## Represent each side as a function of x $$ \begin{aligned} y &= x^3 - 10x \ y &= x^2 - 6 \end{aligned} $$ ## Formulate the system of equations $$ \begin{cases} y = x^3 - 10x \ y = x^2 - 6 \end{cases} $$

(A) $\begin{aligned} y &= x^3 - x^2 + 10x + 6 \ y &= 0 \end{aligned}$

(B) $\begin{aligned} y &= x^3 - x^2 + 10x \ y &= 6 \end{aligned}$

(C) $\begin{aligned} y &= x^3 - 10x \ y &= x^2 - 6 \end{aligned}$

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

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QUESTION IMAGE

Question

Explanation:

Identify the given equation

Represent each side as a function of x

Formulate the system of equations

Answer: