Question

What two numbers add to be 6 and multiply to be 15

Answer 1

   
$\displaystyle \bf \\ x_1+x_2=6\\\\ x_1\cdot x_2=15\\\\ \Longrightarrow~~x^2-6x+15=0\\\\ x_{12}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{6\pm\sqrt{36-60}}{2}=\\\\ =\frac{6\pm\sqrt{-24}}{2}=\frac{6\pm2\sqrt{-6} }{2}=3\pm i\sqrt{6}\\\\ x_1=\boxed{3-i\sqrt{6}}\\\\ x_2=\boxed{3+i\sqrt{6}}\\\\ \texttt{Verify:}\\\\ x_1+x_2=3-\underline{i\sqrt{6}}+3+\underline{i\sqrt{6}}=3+3=6~~correct\\\\ x_1\cdot x_2=(3-i\sqrt{6})(3+i\sqrt{6})=3^2-(i\sqrt{6})^2=9+6=15~~correct$