find the two numbers whose product is 6 and their sum is -7.

value: 1

a. 1 and 6
b. -1 and 6
c. 1 and -6
d. -1 and -6

Question

find the two numbers whose product is 6 and their sum is -7.

value: 1

a. 1 and 6
b. -1 and 6
c. 1 and -6
d. -1 and -6

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Quadratic Equations" ], "new_concepts": [], "current_concepts": [ "Quadratic Equations" ] } ## Identify the system of equations Using the *Quadratic Equations* knowledge point $$ \begin{cases} a \cdot b = 6 \ a + b = -7 \end{cases} $$ ## Solve for the two numbers Using the *Quadratic Equations* knowledge point $$ \begin{aligned} &t^2 - (a+b)t + ab = 0 \ &t^2 + 7t + 6 = 0 \ &(t+1)(t+6) = 0 \ &t = -1 \quad \text{or} \quad t = -6 \end{aligned} $$ Thus, the two numbers are $-1$ and $-6$.

a. 1 and 6

b. -1 and 6

c. 1 and -6

d. -1 and -6

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the system of equations

Solve for the two numbers

Answer: