Question

Find the value of discriminant for each of the following equations.
(1) $2y^2-y+2=0$
(2) $5m^2-m=0$
(3) $\sqrt{5}{x}^2-x-\sqrt{5}=0$

Answer 1

(1) $2y^2-y+2=0$
For the quadratic equation, $a{x}^2+bx+c=0$
$D=b^2-4ac$
Here,
$$\begin{gathered} a=2,b=-1,c=2 \\ D={\left(-1\right)}^2-4\times 2\times 2=1-16=-15 \end{gathered}$$

(2) $5m^2-m=0$
For the quadratic equation, $a{x}^2+bx+c=0$
$D=b^2-4ac$
Here,
$$\begin{gathered} m=5,b=-1,c=0 \\ D={\left(-1\right)}^2-4\times 5\times 0=1 \end{gathered}$$

(3) $\sqrt{5}{x}^2-x-\sqrt{5}=0$
For the quadratic equation, $a{x}^2+bx+c=0$
$D=b^2-4ac$
Here,
$$\begin{gathered} a=\sqrt{5},b=-1,c=-\sqrt{5} \\ D={\left(-1\right)}^2-4\times \left(\sqrt{5}\right)\times \left(-\sqrt{5}\right) \\ =1+20=21 \end{gathered}$$