polynomial equations!

**mankvill** · June 17th 2008, 09:43 PM

This is giving me some trouble and I need an answer soon.

The equation is: x^2 - 6x + 38

And there are 2 answers, which I assume is b + something, and b - something.

I just don't get it.

Thanks in advance.

**Reckoner** · June 17th 2008, 09:55 PM

Originally Posted by mankvill

The equation is: x^2 - 6x + 38

This is not an equation, it is an expression. Did you mean $x^2 - 6x + 38 = 0$ ?

If that's the case, then this equation has no solutions over the reals since the discriminant, $b^2 - 4ac = 6^2 - 4\cdot1\cdot38 = -116$ , is negative. If you want to find the complex solutions, use the quadratic formula:

$x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a} = \frac{6\pm\sqrt{36-152}}{2}$

$= 3\pm\frac{\sqrt{-116}}2 = 3\pm\frac{i\sqrt{116}}2 = 3\pm\frac{2\sqrt{29}}2\,i$

$\boxed{= 3\pm\sqrt{29}\,i}$

**mankvill** · June 17th 2008, 09:56 PM

That is what I meant, thank you very much!

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