Final Answer:
The discriminant (b^2 - 4ac) for the given quadratic equation is d. 23.
Step-by-step explanation:
The quadratic formula provides a method to find the solutions of a quadratic equation, and the discriminant (b^2 - 4ac) is a key determinant of the nature of these solutions. In the given equation, the coefficients are plugged into the formula, resulting in the discriminant being calculated as 23.
The discriminant is crucial in determining the nature of the roots. If the discriminant is positive, the equation has two distinct real roots. In this case, with a discriminant of 23, we can infer that the quadratic equation has two real solutions. These solutions could be irrational or rational but will be distinct.
Conversely, if the discriminant is zero, the quadratic equation has one real root, indicating a tangent point on the graph. If the discriminant is negative, the equation has two complex conjugate roots, implying that the graph does not intersect the x-axis. The positive value of 23 here ensures that the equation has two real and distinct solutions.
In summary, the discriminant of 23 signifies that the quadratic equation has two real and distinct solutions, providing valuable insight into the nature of the roots and the behavior of the corresponding graph.