Question

question
use the quadratic formula to solve. express your answer in simplest form.
2k² + 11k + 12 = 0

Explanation:

Step1: Recall Quadratic Formula

For \(ax^2 + bx + c = 0\), solutions are \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\). Here, \(a = 2\), \(b = 11\), \(c = 12\).

Step2: Calculate Discriminant

Discriminant \(D=b^2 - 4ac=(11)^2-4(2)(12)=121 - 96 = 25\).

Step3: Substitute into Formula

\(k=\frac{-11\pm\sqrt{25}}{2(2)}=\frac{-11\pm5}{4}\).

Step4: Find Two Solutions

First solution: \(k=\frac{-11 + 5}{4}=\frac{-6}{4}=-\frac{3}{2}\).
Second solution: \(k=\frac{-11 - 5}{4}=\frac{-16}{4}=-4\).

Answer:

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