match the items.

a. $x^2 + 15 = 0$
b. 2
c. 1
d. 0
e. $x^2 - 169 = 0$

1. $x^2 + 6 = 0$
2. $x^2 - 16 = 0$
3. $x^2 + 5 = 5$
4. 0
5. 2

Question

match the items.

a. $x^2 + 15 = 0$
b. 2
c. 1
d. 0
e. $x^2 - 169 = 0$

1. $x^2 + 6 = 0$
2. $x^2 - 16 = 0$
3. $x^2 + 5 = 5$
4. 0
5. 2

Accepted Answer

{ "quality": "clear", "question_count": 5, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Equations", "Difference of Squares" ], "new_concepts": [ "Number of Real Solutions", "Discriminant of Quadratic" ], "current_concepts": [ "Quadratic Equations", "Difference of Squares", "Number of Real Solutions" ] } ## Determine the number of real solutions for each quadratic equation $$ \begin{aligned} &\text{For } 1. \ x^2 + 6 = 0 \implies x^2 = -6 \quad (\text{No real solutions}) \implies 0 \text{ real solutions} \quad \text{(Matches d)} \ &\text{For } 2. \ x^2 - 16 = 0 \implies x^2 = 16 \implies x = \pm 4 \quad (2 \text{ real solutions}) \implies 2 \text{ real solutions} \quad \text{(Matches b)} \ &\text{For } 3. \ x^2 + 5 = 5 \implies x^2 = 0 \implies x = 0 \quad (1 \text{ real solution}) \implies 1 \text{ real solution} \quad \text{(Matches c)} \end{aligned} $$ ## Match the remaining items $$ \begin{aligned} &\text{For } 4. \ 0 \quad (\text{Number of real solutions for } x^2 + 15 = 0 \text{ since } x^2 = -15) \implies \text{Matches a} \ &\text{For } 5. \ 2 \quad (\text{Number of real solutions for } x^2 - 169 = 0 \text{ since } x^2 = 169) \implies \text{Matches e} \end{aligned} $$ | No. | Problem | Answer | |---|---|---| | 1 | $x^2 + 6 = 0$ | d | | 2 | $x^2 - 16 = 0$ | b | | 3 | $x^2 + 5 = 5$ | c | | 4 | 0 | a | | 5 | 2 | e | { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Determine the number of real solutions for each quadratic equation

Match the remaining items

Answer:

No.	Problem	Answer
2	\(x^2 - 16 = 0\)	b
3	\(x^2 + 5 = 5\)	c
4	0	a
5	2	e