[tex] x^{2}+12x+31=0\\ \Delta=b^{2}-4ac=(12)^{2}-4*1*31=144-124=20\\
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-12-\sqrt{20}}{2}=\frac{-12-\sqrt{4*5}}{2}=\frac{-12-2\sqrt{5}}{2}=\frac{2(-6-\sqrt{5})}{2}=-6-\sqrt{5} \\
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-12+\sqrt{20}}{2}=\frac{-12+\sqrt{4*5}}{2}=\frac{-12+2\sqrt{5}}{2}=\frac{2(-6+\sqrt{5})}{2}=-6+\sqrt{5} [/tex]
Numarul real pentru care este valoarea expresiei x²+12x+31 este minima e: -6-√5
