This Quadratic factorises nicely...
$\displaystyle \displaystyle 3x^2 - 4x + 1 = 0$
$\displaystyle \displaystyle 3x^2 - 3x - x + 1 = 0$
$\displaystyle \displaystyle 3x(x - 1) - 1(x - 1)= 0$
$\displaystyle \displaystyle (x - 1)(3x - 1) = 0$
$\displaystyle \displaystyle x -1 = 0$ or $\displaystyle \displaystyle 3x - 1 = 0$
$\displaystyle \displaystyle x = 1$ or $\displaystyle \displaystyle x = \frac{1}{3}$.
Yes it is, but here is an easier way without the formula
You can do this:
$\displaystyle 3x^2 -4x + 1 = 0$
So if you know how to do quadratic equations, you must have a 3 and a 1 in the brackets to achieve the $\displaystyle 3x^2$
Therefore your looking at:
$\displaystyle (3x ...)(x ...)$
Obviously the factors of 1, is 1 and itself so you can get:
$\displaystyle (3x .. 1)(x .. 1)$
Now about the signs, you need a + 1, so you need either 2 +'s or 2 -'s, seeing as you have -4 in the middle you can achieve this with 2 -'s
so:
$\displaystyle (3x - 1)(x - 1) = 0$
$\displaystyle x = 1 or x = 1/3$
Regards
Strictly speaking, "0.33" is NOT a correct answer- $\displaystyle \frac{1}{3}$ is.
0.33 is only approximately equal to 1/3.
Also, you should understand that you could have checked these by simply substituting you answers into the given equation.
If x= 1, then $\displaystyle 3x^2- 4x+ 1= 3(1)^2- 4(1)+ 1= 3- 4+ 1= 0$ and $\displaystyle 3\left(\frac{1}{3}\right)^2- 4\left(\frac{1}{3}\right)+ 1= \fra{1}{3}- \frac{4}{3}+ 1= 0$.
And, as others have pointed out, if a polygon can be factored, that is a better way of solving it than using a formula.