Solution assignment 09 Quadratic equations (abc-formula)

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Assignment 9

For which value(s) of  does the equation:

have two coinciding solutions .

Solution

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:

or:

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:

or

We can also get the same result by solving:

but quite often the negative solution will be forgotten.

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