To find the discriminant of the quadratic equation, we need to identify the standard form of the equation, which is ax² + bx + c = 0. In this case, the given equation is:
6x² + 4x + 3 = 0
Based on this equation, we can identify the coefficients:
- a = 6 (the coefficient of x²)
- b = 4 (the coefficient of x)
- c = 3 (the constant term)
The formula for the discriminant (D) is:
D = b² – 4ac
Now, let’s plug in the values of a, b, and c into the equation:
D = (4)² – 4(6)(3)
D = 16 – 72
D = -56
This means that the discriminant of the given quadratic equation is -56.
A negative discriminant indicates that the quadratic equation does not have real roots. Instead, it has two complex conjugate roots. In practical terms, this means that if you were to graph the quadratic function represented by this equation, the parabola would not intersect the x-axis, showing only its vertex and the curve itself.
In summary, the discriminant of the quadratic equation 6x² + 4x + 3 is -56, indicating the presence of complex roots.