# How do you determine the value of k so that 4x^2 + 24x + k = 0 has discriminant zero?

Mar 19, 2017

$k = \textcolor{g r e e n}{36}$

#### Explanation:

For the general quadratic: $a {x}^{2} + b x + c = 0$
the discriminant is
$\textcolor{w h i t e}{\text{XXX}} \Delta = {b}^{2} - 4 a c$

For the specific quadratic: $4 {x}^{2} + 24 x + k = 0$
the discriminant is
$\textcolor{w h i t e}{\text{XXX}} \Delta = {24}^{2} - 4 \cdot 4 \cdot k$

If we want the discriminant to be zero:
$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{{24}^{2}} - \textcolor{m a \ge n t a}{4 \cdot 4 \cdot k} = 0$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow \textcolor{b l u e}{\left({4}^{2}\right) \cdot \left({6}^{2}\right)} - \textcolor{m a \ge n t a}{\left({4}^{2}\right) \cdot k} = 0$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow {6}^{2} - k = 0$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow k = {6}^{2} = 36$