Question

Determine the nature of the root of the quadratic equation.

`sqrt 3 x^2 + sqrt 2 x - 2 sqrt 3 = 0`

Answer 1

Comparing `sqrt 3 x^2 + sqrt 2 x - 2 sqrt 3 = 0` with ax² + bx + c = 0.

We get, 

`a = sqrt 3`, `b = sqrt 2`, `c = -2 sqrt 3`,

Δ = b² − 4ac

= `(sqrt 2)^2 - 4(sqrt 3)(-2 sqrt3)`

= 2 + 24

Δ = 26

Δ > 0

∴ The roots are real and unequal.