Which of the following equations has imaginary roots ?

1. x² + 10x - 3 = 0

2. 2x² - 5x + 9 = 0

3. x² + 5x + 4 = 0

4. 5x² - 8x - 1 = 0

Comparing equation x² + 10x - 3 = 0, with ax² + bx + c = 0, we get :

a = 1, b = 10 and c = -3.

By formula,

D = b² - 4ac

= (10)² - 4 × 1 × -3

= 100 + 12

= 112; which is positive.

Comparing equation 2x² - 5x + 9 = 0, with ax² + bx + c = 0, we get :

a = 2, b = -5 and c = 9.

By formula,

D = b² - 4ac

= (-5)² - 4 × 2 × 9

= 25 - 72

= -47; which is negative.

∴ Roots are imaginary.

Hence, Option 2 is the correct option.