Answer
$k= -4.72,k= 2.42$
Work Step by Step
Use the square root method. Use the quadratic formula.
$$
k^2+2.3 k-11.4=0.
$$ $$
\begin{aligned}
& a=1 \\
& b=2.3 \\
& c=-11.4
\end{aligned}
$$ $$
\begin{aligned}
k & =\frac{-b \pm \sqrt{b^2-4 a c}}{2 a} \\
& =\frac{-2.3 \pm \sqrt{2.3^2+4 \cdot 11.4}}{2} \\
& =\frac{-2.3 \pm \sqrt{50.89}}{2} \\
& \approx \frac{-2.3 \pm 7.1337}{2}
\end{aligned}
$$ $$
\begin{aligned}
k & =\frac{-2.3-7.1337}{2} \\
& =-4.72
\end{aligned}
$$ $$
\begin{aligned}
k& =\frac{-1.4+7.846}{2} \\
& =2.42
\end{aligned}
$$ Define the following version of the function and plot it. We see that the zeros are where they should be.
$$ h(k) =k^2+2.3 k-11.4$$
