Question

Without solving, comment upon the nature of roots of the following equation: 

`x^2 + 2sqrt(3)x - 9 = 0`

Answer 1

`x^2 + 2sqrt(3)x - 9 = 0`

a = 1, b = `2sqrt(3)` and c = −9

∴ Discriminant (Δ) = b² – 4ac 

= `(2sqrt3)^2 - 4(1) (-9)`

= 4 × 3 + 36

= 12 + 36

= 48

Since D = 48 and 48 > 0.

The roots are real and distinct.

Since 48 is not a perfect square, its roots are irrational.