The nature of roots of the quadratic equation 4x² – 12x – 9 = 0 is :

The nature of roots of the equation can be found out using the following formula:

⟹ b² – 4ac

When we compare the above quadratic equation with the generalized one we get,

ax² + bx + c = 0

∴ a = 4

b = -12

c = -9

⟹ b² – 4ac

⟹ (-12)² – (4 × -9 × 4)

⟹ 144 – (-144)

⟹ 144 + 144

= 288

Since b² – 4ac>0, the roots will be real and distinct.

So the correct answer is B [real and distinct].