The discriminant of a quadratic equation provides valuable information about the nature of its roots. For the general form of a quadratic equation,
ax² + bx + c = 0, the discriminant (D) is calculated using the formula: D = b² – 4ac.
In the case of the quadratic equation 2x² + 3x + 5 = 0, we can identify the coefficients as follows:
- a = 2
- b = 3
- c = 5
Plugging these values into the discriminant formula, we have:
D = (3)² – 4(2)(5) = 9 – 40 = -31.
A negative discriminant (D < 0) indicates that the quadratic equation has no real roots; instead, it possesses two complex roots. In practical terms, this means that if you were to graph the equation, the parabola it represents would not intersect the x-axis at any point.
To summarize, for the quadratic equation 2x² + 3x + 5 = 0, the discriminant is -31, which tells us that it has two complex roots, offering insights into the behavior of the equation in the context of real number solutions.