Question

In the following, determine whether the given quadratic equation have real roots and if so, find the roots:

`2x^2-2sqrt6x+3=0`

Answer 1

a = 2

b = `-2sqrt6`

c = 3

Find the Discriminant

D = b² – 4ac

`D = (-2sqrt6)^2 - 4 (2)(3)`

D = (4 × 6) – 24

D = 24 – 24

D = 0

Since D = 0, the quadratic equation has two real and equal roots.

`x = (-b +- sqrtD)/2a`

`x = (-(-2sqrt6))/(2(2))`

`x = (2sqrt6)/4`

`x = sqrt6/2`