Calculate the discriminant and use it to determine how many real-number roots the equation has

3x^ (2) - 6x+4=0

Discriminant = b^2 - 4ac

= (-6) ^2 - (4*3*4)

= - 12

Discriminant < 0

Thus it implies, No real roots for the equation.

The quadratic formula is:

x = (-b±√ (b^2-4ac)) / (2a) for the quadratic of the form ax^2+bx+c

The discriminant is the (b^2-4ac) part of the quadratic formula.

Let d = (b^2-4ac). If:

d<0: There are no real roots.

d=0: There is one real root.

d>0: There are two real roots.

In this case the discriminant is:

(-6) ^2-4*3*4

36-48

-12

Since - 12<0 there are no real roots for the equation 3x^2-6x+4.