Descibe the quadratic equation with two solutions,one solution and no solution.
All quadratic equations have two solutions.
When there is only one solution, there are also two solutions. Such a solution is called a double root.
When there is no solution, there are also two solutions, both of them complex.
Any quadratic equation can be factorised.
Let the quadratic be ax^2 + bx + c = 0
Sometines, this expression can be simply factorised into (x - r1)(x - r2) = 0.
In such a case, you will have two real roots, x = r1, and x = r2.
Sometimes the expression can be factorised into a complete square, e.g. (x - r)^2 = 0.
This is when you will have a double root, x = r (twice).
For the complex case, this will mean that the discriminant is negative. i.e. b^2 - 4ac < 0.
You will now still have two solutions, They will be of the form: x = u + i.v, and x = u - i.v, where i = sqrt(-1).
N.B. note that the above two solutions are complex conjugates . (They will always be so.)