Question

Write the discriminant of the following:

$3\sqrt{3}{x}^2+10x+\sqrt{3}=0$

Answer 1

Step 1:

Comparison of the coefficients:

Compare the coefficients of the given equation with the standard quadratic equation, $a{x}^2+bx+c=0$.

$\begin{array}{rcl}a& =& 3\sqrt{3}\\ b& =& 10\\ c& =& \sqrt{3}\end{array}$

Step 2:

Find the discriminant:

The discriminant $D$ of the given equation can be calculated as,

$\begin{array}{rcl}D& =& b^2-4ac\\ & =& {\left(10\right)}^2-\left(4\times 3\sqrt{3}\times \sqrt{3}\right)\\ & =& 100-\left(4\times 3\times 3\right)\\ & =& 100-36\\ & =& 64\end{array}$

Hence, the discriminant of the given equation is $D=64$.