Solution 2.3:4c

From Förberedande kurs i matematik 1

(Difference between revisions)
Jump to: navigation, search
m (Lösning 2.3:4c moved to Solution 2.3:4c: Robot: moved page)
Line 1: Line 1:
-
{{NAVCONTENT_START}}
+
The equation
-
<center> [[Image:2_3_4c.gif]] </center>
+
<math>\left( x-\text{3} \right)\left( x-\sqrt{\text{3}} \right)=0</math>
-
{{NAVCONTENT_STOP}}
+
is a second-degree equation which has
 +
<math>x=\text{3 }</math>
 +
and
 +
<math>x=\sqrt{\text{3}}</math>
 +
as roots; when
 +
<math>x=\text{3 }</math>, the first factor is zero and when
 +
<math>x=\sqrt{\text{3}}</math>
 +
the second factor is zero.
 +
 
 +
If we expand the equations left-hand side, we get the equation in standard form,
 +
 
 +
 
 +
<math>\begin{align}
 +
& \left( x-\text{3} \right)\left( x-\sqrt{\text{3}} \right)=x^{2}-\sqrt{\text{3}}x-3x+3\sqrt{\text{3}} \\
 +
& =x^{2}-\left( 3+\sqrt{\text{3}} \right)x+3\sqrt{\text{3}}=0 \\
 +
\end{align}</math>
 +
 
 +
 
 +
NOTE: the general answer is,
 +
 
 +
 
 +
<math>ax^{2}-\left( 3+\sqrt{\text{3}} \right)ax+3\sqrt{\text{3}}a=0</math>
 +
 
 +
 
 +
where
 +
<math>a\ne 0</math>
 +
is a constant.

Revision as of 09:38, 21 September 2008

The equation \displaystyle \left( x-\text{3} \right)\left( x-\sqrt{\text{3}} \right)=0 is a second-degree equation which has \displaystyle x=\text{3 } and \displaystyle x=\sqrt{\text{3}} as roots; when \displaystyle x=\text{3 }, the first factor is zero and when \displaystyle x=\sqrt{\text{3}} the second factor is zero.

If we expand the equations left-hand side, we get the equation in standard form,


\displaystyle \begin{align} & \left( x-\text{3} \right)\left( x-\sqrt{\text{3}} \right)=x^{2}-\sqrt{\text{3}}x-3x+3\sqrt{\text{3}} \\ & =x^{2}-\left( 3+\sqrt{\text{3}} \right)x+3\sqrt{\text{3}}=0 \\ \end{align}


NOTE: the general answer is,


\displaystyle ax^{2}-\left( 3+\sqrt{\text{3}} \right)ax+3\sqrt{\text{3}}a=0


where \displaystyle a\ne 0 is a constant.

Retrieved from "http://wiki.sommarmatte.se/wikis/2008/bridgecourse1-ImperialCollege/index.php/Solution_2.3:4c"