For which value(s) of does the equation:
have two coinciding solutions .
In order to find out whether a quadratic equation has two different solutions, one (two coinciding) solution or no (real) solution at all we have to look at the discriminant. In this case:
The equation has two coinciding solutions if:
We can calculate the values of by solving the equation. This can be done in two different ways.
We can apply the special product:
In this case this means:
and thus the solutions are:
We can also get the same result by solving:
but quite often the negative solution will be forgotten.