Factorize the following expression : \(x^2 – 3x – 6\)
\[
x^2 – 3x – 6
\]
\[
= x^2 – \frac{3 + \sqrt{33}}{2}x + \frac{-3 + \sqrt{33}}{2}x – 6
\]
\[
= x\left(x – \frac{3 + \sqrt{33}}{2}\right)
+ \frac{-3 + \sqrt{33}}{2}
\left(x – \frac{3 + \sqrt{33}}{2}\right)
\]
\[
= \left(x – \frac{3 + \sqrt{33}}{2}\right)
\left(x + \frac{-3 + \sqrt{33}}{2}\right)
\]
\[
= \left(x – \frac{3 + \sqrt{33}}{2}\right)
\left(x – \frac{3 – \sqrt{33}}{2}\right)
\]