Hi,

I have been trying to factorise the above, but simply cannot find a solution.

Thanks for any help.

Printable View

- Dec 17th 2011, 12:02 AMbermudjfactorising x^2 - x + 4
Hi,

I have been trying to factorise the above, but simply cannot find a solution.

Thanks for any help. - Dec 17th 2011, 12:07 AMFernandoRevillaRe: factorising x^2 - x + 4
- Dec 17th 2011, 04:23 AMProve ItRe: factorising x^2 - x + 4
$\displaystyle \displaystyle \begin{align*} x^2 - x + 4 &= x^2 - x + \left(-\frac{1}{2}\right)^2 - \left(-\frac{1}{2}\right)^2 + 4 \\ &= \left(x - \frac{1}{2}\right)^2 - \frac{1}{4} + \frac{16}{4} \\ &= \left(x - \frac{1}{2}\right)^2 + \frac{15}{4} \\ &= \left(x - \frac{1}{2}\right)^2 - \left(\frac{i\sqrt{15}}{2}\right)^2 \\ &= \left(x - \frac{1}{2} - \frac{i\sqrt{15}}{2}\right)\left(x - \frac{1}{2} + \frac{i\sqrt{15}}{2}\right) \end{align*}$