Question

Find the discriminant of the following equation and
hence find nature of roots Also find them, If
they are real
x^2-1/2x-4=0​

Answer 1

$x ^{2} - \frac{1}{2} x - 4 \\ 2 {x}^{2} - x - 8 \\ disciminant = b {}^{2} - 4ac \\ = ( - 1) {}^{2} - 4(2)( - 8) \\ = 1 + 64 \\ = 65 \\ since \: 65 \: is \: not \: a \: perfect \: square \\ \: therefore \: roots \: of \: the \: give \: \\ quadratic \: equation \: is \: not \: real$