The quadratic has no real solutions.
A quadratic equation can have either two real solutions or no real solutions.
If the discriminant of a quadratic equation is less then 0 then it will have no real solutions.
It will then have two equal real solutions
There are two distinct real solutions.
A cubic has from 1 to 3 real solutions. The fact that every cubic equation with real coefficients has at least 1 real solution comes from the intermediate value theorem. The discriminant of the equation tells you how many roots there are.
An equation with a degree of three typically has three solutions. However, it is possible for one or more of those solutions to be repeated or complex.
Two distinct real solutions.
There are no real solutions because the discriminant of the quadratic equation is less than zero.
0 real solutions. There are other solutions in the complex planes (with i, the imaginary number), but there are no real solutions.
imaginary
discriminant