The discriminant of a quadratic equation is a key value that helps to determine the nature of the roots of the equation. For a standard quadratic equation of the form ax² + bx + c = 0, the discriminant (D) is calculated using the formula:
D = b² – 4ac
In your case, the equation is 6x² + 4x + 3 = 0. Here:
- a = 6
- b = 4
- c = 3
Substituting these values into the discriminant formula:
D = (4)² – 4(6)(3)
Calculating further, we find:
D = 16 – 72
D = -56
The discriminant, in this case, is -56. Since the discriminant is negative, this indicates that the quadratic equation has no real roots; instead, it has two complex roots. This means that the graph of the equation does not cross the x-axis, confirming that the roots are indeed imaginary.