# Math Help - Finding roots a+bi form

1. ## Finding roots a+bi form

Find the roots in simplest a+bi form y=2x^2-4x+5

[Math]\frac{-b+-\sqrt{ b^2-4ac}}{2a}[/tex]

[Math]\frac{4+-\sqrt{16-4(2)(5)}}{2(2)}[/tex]

[Math]\frac{4+-\sqrt{24}}{4}[/tex]

to put in a+bi form I believe that that it has to be a perfect square and that I can not have a radical in the answer? Please help with what I am missing Thanks

2. Originally Posted by IDontunderstand
Find the roots in simplest a+bi form y=2x^2-4x+5

$\frac{-b+-{{Sqrt}b^2-4ac}}{2a}$
As you (kind of) put down the roots of $ax^2+bx+c$ are $x=\frac{b\pm\sqrt{b^2-4ac}}{2a}$

So we can see that the solutions of $\overbrace{2}^{a}x^2-\overbrace{4}^{b}x+\overbrace{5}^{c}$ are $x=\frac{4\pm\sqrt{(-4)^2-4(2)(5)}}{2(2)}=\frac{4\pm\sqrt{16-40}}{4}=\frac{4\pm2\sqrt{6}i}{4}$

$\frac{4\pm2\sqrt{6}i}{4} = \frac{4}{4}\pm \frac{2\sqrt{6}}{4}i$