in this activity, you will solve quadratic equations using different methods. make sure to use the method that you are asked for in each part.

question 1
solve the two equations in the table by factoring. then enter those factors and the solutions in the table.

\begin{tabular}{|c|c|c|}
\hline
equation & factors & solutions \\
\hline
x^2 + 10 = 0 & & \\
\hline
4x^2 + 25 = 0 & & \\
\hline
\end{tabular}

Question

in this activity, you will solve quadratic equations using different methods. make sure to use the method that you are asked for in each part.

question 1
solve the two equations in the table by factoring. then enter those factors and the solutions in the table.

\begin{tabular}{|c|c|c|}
\hline
equation & factors & solutions \\
\hline
x^2 + 10 = 0 & & \\
\hline
4x^2 + 25 = 0 & & \\
\hline
\end{tabular}

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Quadratic Equations", "Complex Numbers", "Sum of Squares" ], "new_concepts": [], "current_concepts": [ "Solving Quadratic Equations", "Complex Numbers", "Sum of Squares", "Factoring Polynomials" ] } ## Factor and solve the first equation $$ \begin{aligned} &x^2 + 10 = 0 \ &x^2 - (i\sqrt{10})^2 = 0 \ &(x + i\sqrt{10})(x - i\sqrt{10}) = 0 \ &x = \pm i\sqrt{10} \end{aligned} $$ ## Factor and solve the second equation $$ \begin{aligned} &4x^2 + 25 = 0 \ &(2x)^2 - (5i)^2 = 0 \ &(2x + 5i)(2x - 5i) = 0 \ &x = \pm \frac{5}{2}i \end{aligned} $$ | Equation | Factors | Solutions | | :--- | :--- | :--- | | $x^2 + 10 = 0$ | $(x + i\sqrt{10})(x - i\sqrt{10})$ | $x = i\sqrt{10}, -i\sqrt{10}$ | | $4x^2 + 25 = 0$ | $(2x + 5i)(2x - 5i)$ | $x = \frac{5}{2}i, -\frac{5}{2}i$ | { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Factor and solve the first equation

Factor and solve the second equation

Answer: