We are given a quadratic equation $ax^2 + bx + c = 0$ and its discriminant $b^2 - 4ac = -1$. We need to determine the nature of the solutions based on the discriminant's value.

1. Problem Description

We are given a quadratic equation $ax^2 + bx + c = 0$ and its discriminant $b^2 - 4ac = -1$. We need to determine the nature of the solutions based on the discriminant's value.

2. Solution Steps

The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by $\Delta = b^2 - 4ac$. The nature of the roots depends on the value of the discriminant:

* If $\Delta > 0$, the quadratic equation has two distinct real roots.

* If $\Delta = 0$, the quadratic equation has one real root (a repeated root).

* If $\Delta < 0$, the quadratic equation has no real roots (two complex roots).

In this case, we are given that $b^2 - 4ac = -1$. Since $-1 < 0$, the discriminant is negative. Therefore, the quadratic equation has no real roots.

3. Final Answer

No real solutions.