From Förberedande kurs i matematik 1

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-	{{NAVCONTENT_START}}	+	The equation <math>(x-3)(x-\sqrt{3}\,)=0</math> is a second-degree equation which has <math>x=3</math> and <math>x=\sqrt{3}</math> as roots; when <math>x=3</math>, the first factor is zero and when <math>x=\sqrt{3}</math> the second factor is zero.
-	<center> [[Image:2_3_4c.gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	If we expand the equation's left-hand side, we get the equation in standard form,
		+
		+	{{Displayed math||<math>\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}</math>}}
		+
		+
		+	Note: the general answer is
		+
		+	{{Displayed math||<math>ax^{2}-(3+\sqrt{3}\,)ax+3\sqrt{3}a=0\,,</math>}}
		+
		+	where <math>a\ne 0</math> is a constant.

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Current revision

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.