the equation has exactly 1 real solution.
8-4x=0 -> add 4x to both sides.
8=4 -> divide both sides by 4.
2=x.
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.
If the highest degree of an equation is 3, then the equation must have 3 solutions. Solutions can be: 1) 3 real solutions 2) one real and two imaginary solutions.
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