To find the value of the discriminant for the quadratic equation 3x² + 2x, we first need to identify the coefficients in the standard form of a quadratic equation, which is generally expressed as ax² + bx + c = 0.
Here, we can rewrite the equation:
3x² + 2x = 0 can be interpreted with:
- a = 3
- b = 2
- c = 0
The discriminant (D) of a quadratic equation is given by the formula:
D = b² – 4ac
Now, substituting the values of a, b, and c into the discriminant formula:
D = (2)² – 4(3)(0)
Calculating that gives us:
- D = 4 – 0
- D = 4
Thus, the value of the discriminant for the quadratic equation 3x² + 2x is 4.
This means that the quadratic equation has two distinct real roots. The positive discriminant indicates that the parabola represented by the equation intersects the x-axis at two points, yielding two different solutions for x.