how do you find the root of 3x^2-10x+3

I think that this should be the roots of y=3x^2-10x+3

You need to solve  3x^2-10x+3=0

I would look for 2 numbers that multiply to 3*3=9  and add to -10

this is easy   -9 and -1

now replace the middle term -10x with -9x-1x

 

3x^2-9x-1x+3=0

now factorise in pairs

3x^2-9x     -1x+3=0

3x(x-3)      -1(x-3)=0

       (3x-1)(x-3)     =0

so     3x-1=0       or     x-3=0

            x = 1/3    or       x=3

 

Here is another post like this one

http://web2.0calc.com/questions/grouping-method-and-factorizing-quadratic-equations

at the bottom is a you tube clip on this it is quite good. :)

http://www.youtube.com/watch?v=ZQ-NRsWhOGI