\\delta = b^2 - 4.a.c\quad x = \frac{-b \pm \sqrt{\delta}}{2.a}\
\x^2 + 5x + 6 = 0\
\a = 1, b = 5, c = 6\
\\delta = b^2 - 4ac\
\\delta = 5^2 - 4.1.6\
\\delta = 25 - 24\
\\delta = 1\
\x = \frac{-b \pm \sqrt{\delta}}{2.a}\
\x = \frac{-(5) \pm \sqrt{1}}{2.1}\
\x = \frac{-5 \pm 1}{2}\
\x = \frac{-5 + 1}{2} = \frac{-4}{2} \
ightarrow x = -2\
\x = \frac{-5 - 1}{2} = \frac{-6}{2} \
ightarrow x = -3\

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Fórmula de Bhaskara", "Equação do Segundo Grau" ], "current_concepts": [ "Equação do Segundo Grau", "Fórmula de Bhaskara", "Cálculo do Discriminante" ] } ## Identificar os coeficientes e calcular o discriminante $\Delta$ $$ \begin{aligned} &x^2 + 5x + 6 = 0 \ &a = 1, \quad b = 5, \quad c = 6 \ &\Delta = b^2 - 4ac \ &\Delta = 5^2 - 4 \cdot 1 \cdot 6 \ &\Delta = 25 - 24 = 1 \end{aligned} $$ ## Aplicar a fórmula de Bhaskara para encontrar as raízes $$ \begin{aligned} &x = \frac{-b \pm \sqrt{\Delta}}{2a} \ &x = \frac{-5 \pm \sqrt{1}}{2 \cdot 1} \ &x = \frac{-5 \pm 1}{2} \end{aligned} $$ ## Calcular os valores de $x'$ e $x''$ $$ \begin{aligned} &x' = \frac{-5 + 1}{2} = \frac{-4}{2} = -2 \ &x'' = \frac{-5 - 1}{2} = \frac{-6}{2} = -3 \end{aligned} $$ $x' = -2$ e $x'' = -3$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Equação do Segundo Grau" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identificar os coeficientes e calcular o discriminante \(\Delta\)

Aplicar a fórmula de Bhaskara para encontrar as raízes

Calcular os valores de \(x'\) e \(x''\)

Answer: