Question

Find the value of discriminant of the following equation.

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

Answer 1

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

For the quadratic equation,  $$a{x}^2+bx+c=0$$

$$D=b^2-4ac$$

Here,

$$a=\sqrt{5},b=-1,c=-\sqrt{5}$$
$$D={(-1)}^2-4\times \left(\sqrt{5}\right)\times (-\sqrt{5})$$
$$=1+20=21$$