Question

Discriminant of the quadratic equation $\sqrt{5}{x}^2-3\sqrt{3}x-2\sqrt{5}=0$ is

• A. $67$
• B. $76$
• C. $-67$
• D. $-76$

Answer 1

The correct option is A

$67$

Explanation for correct option:

Step1: Discriminant

For any quadratic equation,

$a{x}^2+bx+c=0$

Discriminant is given by,$\mathit{D}\mathbf{=}{\mathit{b}}^{\mathbf{2}}\mathbf{-}\mathbf{4}\mathit{a}\mathit{c}$

Step2: Finding discriminant of equation.

Given equation,

$\sqrt{5}{x}^2-3\sqrt{3}x-2\sqrt{5}=0$

Using the discriminant formula,

Here, $b=-3\sqrt{3},a=\sqrt{5,}\&c=-2\sqrt{5}$

Therefore,

$\begin{array}{rcl}D& =& {(-3\sqrt{3})}^2-4\times \sqrt{5}\times (-2\sqrt{5})\mathbf{}\mathit{D}\mathbf{=}{\mathit{b}}^{\mathbf{2}}\mathbf{-}\mathbf{4}\mathit{a}\mathit{c}\\ D& =& 40+27\\ D& =& 67\end{array}$

Hence, Correct option is $\mathbf{\left(}\mathit{A}\mathbf{\right)}$.