what is the solution set of the quadratic inequality $x^2 - 5 \le 0$?

$\circ$ $\{x \mid -5 \le x \le 5\}$
$\circ$ $\{x \mid -\sqrt{5} \le x \le 5\}$
$\circ$ $\{x \mid -5 \le x \le \sqrt{5}\}$
$\circ$ $\{x \mid -\sqrt{5} \le x \le \sqrt{5}\}$

Question

what is the solution set of the quadratic inequality $x^2 - 5 \le 0$?

$\circ$ $\{x \mid -5 \le x \le 5\}$
$\circ$ $\{x \mid -\sqrt{5} \le x \le 5\}$
$\circ$ $\{x \mid -5 \le x \le \sqrt{5}\}$
$\circ$ $\{x \mid -\sqrt{5} \le x \le \sqrt{5}\}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Inequalities" ], "new_concepts": [], "current_concepts": [ "Quadratic Inequalities" ] } ## Find the boundary points of the inequality $$ \begin{aligned} x^2 - 5 &= 0 \ x^2 &= 5 \ x &= \pm\sqrt{5} \end{aligned} $$ ## Determine the solution interval $$ \begin{aligned} &\text{For } x^2 - 5 \le 0, \text{ the solution lies between the roots:} \ &-\sqrt{5} \le x \le \sqrt{5} \end{aligned} $$ ## Express in set-builder notation $$ \{x \mid -\sqrt{5} \le x \le \sqrt{5}\} $$

(A) $\{x \mid -5 \le x \le 5\}$

(B) $\{x \mid -\sqrt{5} \le x \le 5\}$

(C) $\{x \mid -5 \le x \le \sqrt{5}\}$

(D) $\{x \mid -\sqrt{5} \le x \le \sqrt{5}\}$

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

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QUESTION IMAGE

Question

Explanation:

Find the boundary points of the inequality

Determine the solution interval

Express in set-builder notation

Answer: