Question

A quadratic equation has a discriminant of -1.

which answer describes the number and type of the solution of the equation?

1 real solution
2 real solution
1 real and 1 complex solution
2 complex solution

Answer 1

We can determine number of solutions of a quadratic equation using the discriminant.
If the discriminant is negative, there is no real solution, meaning that both solutions are complex.

If the discriminant is zero, there is 1 real solution, meaning that the other solution is complex.

If the discriminant is positive, there are 2 real solutions.

In this case, the discriminant is -1 which is negative. So there is no real solution. That means there are two complex solutions.