Question

use the zero - product property to solve the following equation. write your solutions as a set in roster form.
$k^{2}+13k + 40 = 0$
the solution set is
(use a comma to separate answers as needed.)

Explanation:

Step1: Factor the quadratic trinomial

We find two numbers that multiply to $40$ and add to $13$, which are $5$ and $8$.
$k^2 + 13k + 40 = (k + 5)(k + 8) = 0$

Step2: Apply zero-product property

Set each factor equal to 0.
$k + 5 = 0$ or $k + 8 = 0$

Step3: Solve for $k$ in each equation

For $k + 5 = 0$: $k = -5$
For $k + 8 = 0$: $k = -8$

Answer:

$\{-8, -5\}$