The discriminant of a quadratic equation in the standard form ax² + bx + c is given by the formula: D = b² – 4ac. In our equation, 3x² + 6x + 2, the coefficients can be identified as follows: a = 3, b = 6, and c = 2.
Now, we can substitute these values into the discriminant formula:
D = (6)² – 4(3)(2) = 36 – 24 = 12.
Therefore, the discriminant of the quadratic equation 3x² + 6x + 2 is 12. A positive discriminant indicates that there are two distinct real roots for the quadratic equation. This means that if you solve the equation, you will find two different x-values where the parabola intersects the x-axis.