solving quadratic equation - factorization method

example 4

solve: $x^2 - 15x + 56 = 0$

solution

since the coefficient of $x^2$ term is 1, the factors can be written as $(x + a)(x + b) = 0$.

value: 1

find the two numbers whose sum is -15 and their product is 56.

a. 7 and -8
b. -7 and -8
c. -7 and 8
d. 7 and 8

Question

solving quadratic equation - factorization method

example 4

solve: $x^2 - 15x + 56 = 0$

solution

since the coefficient of $x^2$ term is 1, the factors can be written as $(x + a)(x + b) = 0$.

value: 1

find the two numbers whose sum is -15 and their product is 56.

a. 7 and -8
b. -7 and -8
c. -7 and 8
d. 7 and 8

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Equations" ], "new_concepts": [], "current_concepts": [ "Quadratic Equations", "Factoring Quadratics" ] } ## Identify the sum and product requirements $$ \begin{aligned} &a + b = -15 \ &a \cdot b = 56 \end{aligned} $$ ## Test the given options $$ \begin{aligned} &\text{Option a: } 7 + (-8) = -1 eq -15 \ &\text{Option b: } -7 + (-8) = -15, \quad (-7) \cdot (-8) = 56 \ &\text{Option c: } -7 + 8 = 1 eq -15 \ &\text{Option d: } 7 + 8 = 15 eq -15 \end{aligned} $$ ## Select the correct option $$ a = -7, \quad b = -8 $$

a. 7 and -8

b. -7 and -8

c. -7 and 8

d. 7 and 8

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

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QUESTION IMAGE

Question

Explanation:

Identify the sum and product requirements

Test the given options

Select the correct option

Answer: