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

3x^2 - 6x + 1 = 0

three real-number roots

two real-number roots

one real-number root

no real-number roots

In a quadratic equation with the general formula of:

ax^2 + bx + c = 0

The discriminant is equal to b^2 - 4(a)(c). If the answer is a perfect square, then there are two real numbers. If not, then there are no real number root.

The discriminant for this equation is

(-6)^2 - 4(3)(1) = 24

Since 24 is not a perfect square, there are no real number roots.