Lösung 2.3:4c
Aus Online Mathematik Brückenkurs 1
(Unterschied zwischen Versionen)
K (Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel)) |
K (hat „Solution 2.3:4c“ nach „Lösung 2.3:4c“ verschoben: Robot: moved page) |
Version vom 14:11, 22. Okt. 2008
The equation \displaystyle (x-3)(x-\sqrt{3}\,)=0 is a second-degree equation which has \displaystyle x=3 and \displaystyle x=\sqrt{3} as roots; when \displaystyle x=3, the first factor is zero and when \displaystyle x=\sqrt{3} the second factor is zero.
If we expand the equation's left-hand side, we get the equation in standard form,
| \displaystyle \begin{align}
(x-3)(x-\sqrt{3}\,) &= x^{2}-\sqrt{3}x-3x+3\sqrt{3}\\[5pt] &= x^{2}-(3+\sqrt{3}\,)x+3\sqrt{3}=0\,\textrm{.} \end{align} |
Note: the general answer is
| \displaystyle ax^{2}-(3+\sqrt{3}\,)ax+3\sqrt{3}a=0\,, |
where \displaystyle a\ne 0 is a constant.
