Question

question
use the quadratic formula to solve. express your answer in simplest form.
$2k^2 + 11k + 12 = 0$
answer attempt 2 out of 2
additional solution remove solution
$k = -\frac{16}{4}$, $k = -4$ submit answer

Explanation:

Step1: Identify coefficients

For quadratic equation \(ax^2 + bx + c = 0\), here \(a = 2\), \(b = 11\), \(c = 12\).

Step2: Quadratic formula

Quadratic formula: \(k=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\)
Substitute values: \(k=\frac{-11\pm\sqrt{11^2 - 4\times2\times12}}{2\times2}\)

Step3: Calculate discriminant

\(11^2 - 4\times2\times12 = 121 - 96 = 25\)

Step4: Solve for k

\(k=\frac{-11\pm\sqrt{25}}{4}=\frac{-11\pm5}{4}\)
Two solutions:
\(k_1=\frac{-11 + 5}{4}=\frac{-6}{4}=-\frac{3}{2}\)
\(k_2=\frac{-11 - 5}{4}=\frac{-16}{4}=-4\)

Answer:

\(k = -\frac{3}{2}\), \(k = -4\)