The problem states that the quadratic equation $ax^2 + bx + c = 0$ has a discriminant $b^2 - 4ac = -1$. We are asked to determine the nature of the solutions of this equation.

1. Problem Description

The problem states that the quadratic equation $ax^2 + bx + c = 0$ has a discriminant $b^2 - 4ac = -1$. We are asked to determine the nature of the solutions of this equation.

2. Solution Steps

The discriminant, $b^2 - 4ac$, determines the nature of the solutions to a quadratic equation.

If $b^2 - 4ac > 0$, the quadratic equation has two distinct real solutions.

If $b^2 - 4ac = 0$, the quadratic equation has one real solution (a repeated root).

If $b^2 - 4ac < 0$, the quadratic equation has no real solutions. Instead, it has two complex solutions.

In this case, the discriminant is $b^2 - 4ac = -1$, which is less than

0. Therefore, the quadratic equation has no real solutions.

3. Final Answer

d) No real solutions