solving quadratic equations: zero product property

which function has real zeros at $x = -10$ and $x = -6$?

$f(x) = x^2 + 4x + 60$

$f(x) = x^2 + 16x + 60$

$f(x) = x^2 - 16x + 60$

Question

solving quadratic equations: zero product property

which function has real zeros at $x = -10$ and $x = -6$?

$f(x) = x^2 + 4x + 60$

$f(x) = x^2 + 16x + 60$

$f(x) = x^2 - 16x + 60$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Factoring Quadratics", "Zero Product Property", "Roots of Quadratic Functions" ], "new_concepts": [], "current_concepts": [ "Factoring Quadratics", "Zero Product Property", "Roots of Quadratic Functions" ] } ## Set up the factored form of the quadratic function $$ \begin{aligned} x_1 &= -10 \ x_2 &= -6 \ f(x) &= a(x - x_1)(x - x_2) \ f(x) &= a(x - (-10))(x - (-6)) \ f(x) &= a(x + 10)(x + 6) \end{aligned} $$ ## Expand the factors to standard form $$ \begin{aligned} a &= 1 \ f(x) &= (x + 10)(x + 6) \ f(x) &= x^2 + 6x + 10x + 60 \ f(x) &= x^2 + 16x + 60 \end{aligned} $$ ## Match with the given options $$ \begin{aligned} f(x) &= x^2 + 16x + 60 \end{aligned} $$

(A) $f(x) = x^2 + 4x + 60$

(B) $f(x) = x^2 + 16x + 60$

(C) $f(x) = x^2 - 16x + 60$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Roots of Quadratic Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the factored form of the quadratic function

Expand the factors to standard form

Match with the given options

Answer: