The quadratic equation $2x^2 - \sqrt{5}x + 1 = 0$ has

1. two distinct real roots
2. two equal real roots
3. no real roots
4. more than two real roots

In order to find nature of roots we need to find the value of, b² - 4ac

Given,

$2x^2 - \sqrt{5}x + 1 = 0$

Comparing equation with ax² + bx + c = 0
a= 2 , b = -$\sqrt{5}$ , c = 1

Putting values in b² - 4ac

$(-\sqrt{5})^2 - 4 \times 2 \times 1 \\[0.5em] \Rightarrow 5 - 8 \\[0.5em] \Rightarrow -3$

Since, b² - 4ac = -3 < 0 , hence there are no real roots

∴ Option 3 is the correct option.