Question

Why can't x^2-5x-1 be factorable

Answer 1

x² - 5x -1

Applying the quadratic formula:

`\begin{gathered} x_(1,2)=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_(1,2)=\frac{-(-5)\pm\sqrt[]{(-5)^2-4(1)(-1)}}{2(1)} \\ x_(1,2)=\frac{5\pm\sqrt[]{29}}{2} \\ x_1=\frac{5+\sqrt[]{29}}{2}\approx5.193 \\ x_2=\frac{5-\sqrt[]{29}}{2}\approx-0.193 \end{gathered}`

Then, x² - 5x -1 = (x - 5.193)(x + 0.193)