what are the solution(s) of the quadratic equation $98 - x^2 = 0$?

$x = \pm 2\sqrt{7}$

$x = \pm 6\sqrt{3}$

$x = \pm 7\sqrt{2}$

no real solution

Question

what are the solution(s) of the quadratic equation $98 - x^2 = 0$?

$x = \pm 2\sqrt{7}$

$x = \pm 6\sqrt{3}$

$x = \pm 7\sqrt{2}$

no real solution

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Equations", "Quadratic Roots" ], "new_concepts": [ "Simplifying Radicals" ], "current_concepts": [ "Quadratic Equations", "Quadratic Roots", "Simplifying Radicals" ] } ## Isolate the quadratic term $$ \begin{aligned} 98 - x^2 &= 0 \ x^2 &= 98 \end{aligned} $$ ## Apply the square root property $$ \begin{aligned} x &= \pm\sqrt{98} \end{aligned} $$ ## Simplify the radical expression $$ \begin{aligned} x &= \pm\sqrt{49 \times 2} \ x &= \pm7\sqrt{2} \end{aligned} $$

(A) $x = \pm2\sqrt{7}$

(B) $x = \pm6\sqrt{3}$

(C) $x = \pm7\sqrt{2}$

(D) no real solution

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

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QUESTION IMAGE

Question

Explanation:

Isolate the quadratic term

Apply the square root property

Simplify the radical expression

Answer: