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)=(-b\pm√(b^2-4ac))/(2a)=(6\pm√(36-60))/(2)=\\\\ =(6\pm√(-24))/(2)=(6\pm2√(-6) )/(2)=3\pm i√(6)\\\\ x_1=\boxed{3-i√(6)}\\\\ x_2=\boxed{3+i√(6)}\\\\ \texttt{Verify:}\\\\ x_1+x_2=3-\underline{i√(6)}+3+\underline{i√(6)}=3+3=6~~correct\\\\ x_1\cdot x_2=(3-i√(6))(3+i√(6))=3^2-(i√(6))^2=9+6=15~~correct`