The problem describes a quadratic equation $ax^2 + bx + c = 0$ with a discriminant $b^2 - 4ac = -1$. The question asks us to determine the nature of the solutions to this quadratic equation based on its discriminant.

1. Problem Description

The problem describes a quadratic equation $ax^2 + bx + c = 0$ with a discriminant $b^2 - 4ac = -1$. The question asks us to determine the nature of the solutions to this quadratic equation based on its discriminant.

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 (solutions) 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 (or two equal real roots).

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

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

3. Final Answer

d) No real solutions