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Question
Find the value of discriminant of the following equation.
\[\sqrt{5} x^2 - x - \sqrt{5} = 0\]
Solution
\[\sqrt{5} x^2 - x - \sqrt{5} = 0\]
For the quadratic equation, \[a x^2 + bx + c = 0\]
\[D = b^2 - 4ac\]
Here,
\[a = \sqrt{5}, b = - 1, c = - \sqrt{5}\]
\[D = \left( - 1 \right)^2 - 4 \times \left( \sqrt{5} \right) \times \left( - \sqrt{5} \right)\]
\[ = 1 + 20 = 21\]
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