trying to solve 2x(squared) = 3x - 6; do I use 'FOIL'?

[snoopsilver]

I am trying to solve:

2x(squared)=3x-6

I thought I should get the x's on one side but I can't make it work when I do...please help!

 

[galactus]

\(\displaystyle \L\\2x^{2}-3x+6=0\) only has complex solutions. That's probably why you can't make it work.

 

[snoopsilver]

\(\displaystyle \L\\2x^{2}-3x+6=0\) only has complex solutions. That's probably why you can't make it work.

I have to find the sum and the product of its roots and i got what you did but that isn't the answer is it? I mean there is more to it right?

 

[o_O]

There are no solutions. If you think about it graphically, the parabola never crosses the x-axis (where y = 0) telling you that there are no real solutions.

Also, if you plug it into the quadratic formula, you won't get a real answer:

\(\displaystyle \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}\)

 

[galactus]

The solutions are complex.

\(\displaystyle \L\\\frac{3}{4}+\frac{\sqrt{39}}{4}i, \;\ \frac{3}{4}-\frac{\sqrt{39}}{4}i\)

To find the sum of the roots of a quadratic, all you have to do is take the negative of the ratio of the first and second coefficients.

\(\displaystyle \L\\ax^{2}+bx+c\)

The sum of the roots is -b/a.

In your case, add up the complex solutions. I bet you get 3/2.

To find the product of the roots, it's just c/a. See?. You don't have to actually find the roots to get the sum or product. Just know a little trick.