Determine the nature of the roots of the equation $2 x^{2} - 5 x - 1 = 0$

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Solution

This is in the form of $a x^{2} + b x + c = 0$ . The co-efficient are $a = 2, b = - 5, c = - 1$
$△ = b^{2} - 4 a c, △ = (- 5)^{2} - 4 (2) (- 1), △ = 25 + 8, △ = 33$
$∴ △ > 0$ . Therefore, roots are real and distinct

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