Question 75086
<pre><font size = 5><b>
Use the quadratic formula to solve each 
of the following quadratic equations.
{{{3x^2-2x+1=0}}}

My answer to this equation was:
x={{{1/3+(2sqrt(2)/3)*i}}},x={{{1/3-(2sqrt(2)/3)*i}}}.
Is this correct? Thanks for your time. 

'Fraid it isn't. You've got an extra 
"2" factor before the radical.  Let's 
go through it:

The quadratic formula is:
                  ______ 
            -b ± <font face = "symbol">Ö</font>b²-4ac
        x = —————————————
                2a 

where a = 3; b = -2; c = 1

                      _____________ 
             -(-2) ± <font face = "symbol">Ö</font>(-2)²-4(3)(1)
        x = ————————————————————————
                     2(3) 
                  ____ 
             2 ± <font face = "symbol">Ö</font>4-12
        x = ————————————
                 6

                  __ 
             2 ± <font face = "symbol">Ö</font>-8
        x = —————————
                6

                   _ 
             2 ± i<font face = "symbol">Ö</font>8
        x = —————————
                6

                   ___
             2 ± i<font face = "symbol">Ö</font>4·2
        x = ———————————
                 6

                     _
             2    2i<font face = "symbol">Ö</font>2
        x = ——— ± —————
             6      6


                     _
             1     i<font face = "symbol">Ö</font>2
        x = ——— ± —————
             3      3


                   _
             1    <font face = "symbol">Ö</font>2
        x = ——— ± ———·i
             3     3


Edwin</pre>