Lösung 2.3:5a
Aus Online Mathematik Brückenkurs 1
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Version vom 14:11, 22. Okt. 2008
In this exercise we can use the technique for writing equations in factorized form. Consider in our case the equation
| \displaystyle (x+7)(x+7)=0\,\textrm{.} |
This equation has only \displaystyle x=-7 as a root because both factors become zero only when \displaystyle x=-7. In addition, it is an second-degree equation, which we can clearly see if the left-hand side is expanded,
| \displaystyle (x+7)(x+7) = x^{2}+14x+49\,\textrm{.} |
Thus, one answer is the equation \displaystyle x^{2}+14x+49=0\,.
Note: All second-degree equations which have \displaystyle x=-7 as its sole root can be written as
| \displaystyle ax^{2}+14ax+49a=0\,, |
where a is a non-zero constant.
