[Math] Factor polynomial with irrational roots using quadratic equation

Question

If I want to factor the polynomial $x^2 + 3x + 1$, I thought I could use the quadratic formula to find that its roots are $\dfrac{-3\pm\sqrt{5}}{2}$. Then, since those are both negative values, take their positive values as factors, but WolframAlpha said my factorization is not equivalent (see below).
What am I missing?

Answer 1

Try this:

$$\left(x- \frac{-3+\sqrt{5}}{2}\right)\left(x- \frac{-3-\sqrt{5}}{2}\right).$$