question 3
use the quadratic formula to complete the table. to verify your solutions, graph the equations.

\begin{tabular}{|c|c|c|}
\hline
\textbf{equation} & \textbf{value of discriminant} & \textbf{solution value(s)} \\
\hline
(3x^2 + 4x + 4 = 0) & & \\
\hline
(3x^2 + 2x + 4 = 0) & & \\
\hline
\end{tabular}

Question

question 3
use the quadratic formula to complete the table. to verify your solutions, graph the equations.

\begin{tabular}{|c|c|c|}
\hline
\textbf{equation} & \textbf{value of discriminant} & \textbf{solution value(s)} \\
\hline
(3x^2 + 4x + 4 = 0) & & \\
\hline
(3x^2 + 2x + 4 = 0) & & \\
\hline
\end{tabular}

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Discriminant", "Quadratic Formula", "Complex Roots" ], "new_concepts": [], "current_concepts": [ "Discriminant", "Quadratic Formula", "Complex Roots" ] } ## Calculate discriminant and solutions for first equation $$ \begin{aligned} &3x^2 + 4x + 4 = 0 \quad (a=3, b=4, c=4)\ &D = b^2 - 4ac = 4^2 - 4(3)(4) = 16 - 48 = -32\ &x = \frac{-4 \pm \sqrt{-32}}{2(3)} = \frac{-4 \pm 4i\sqrt{2}}{6} = -\frac{2}{3} \pm \frac{2i\sqrt{2}}{3} \end{aligned} $$ ## Calculate discriminant and solutions for second equation $$ \begin{aligned} &3x^2 + 2x + 4 = 0 \quad (a=3, b=2, c=4)\ &D = b^2 - 4ac = 2^2 - 4(3)(4) = 4 - 48 = -44\ &x = \frac{-2 \pm \sqrt{-44}}{2(3)} = \frac{-2 \pm 2i\sqrt{11}}{6} = -\frac{1}{3} \pm \frac{i\sqrt{11}}{3} \end{aligned} $$ | Equation | Value of Discriminant | Solution Value(s) | |---|---|---| | $3x^2+4x+4=0$ | $-32$ | $-\frac{2}{3} \pm \frac{2i\sqrt{2}}{3}$ | | $3x^2+2x+4=0$ | $-44$ | $-\frac{1}{3} \pm \frac{i\sqrt{11}}{3}$ | { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Formula" ] }

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Question

Explanation:

Calculate discriminant and solutions for first equation

Calculate discriminant and solutions for second equation

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