Answer and explanation:
1) Solve : [tex]x^2+9x+2=0[/tex]
Applying quadratic formula,
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Here, a=1 , b=9, c=2
[tex]x=\frac{-9\pm\sqrt{9^2-4(1)(2)}}{2(1)}[/tex]
[tex]x=\frac{-9\pm\sqrt{81-8}}{2}[/tex]
[tex]x=\frac{-9\pm\sqrt{73}}{2}[/tex]
[tex]x=\frac{-9+\sqrt{73}}{2},\frac{-9-\sqrt{73}}{2}[/tex]
[tex]x=-0.227,-8.772[/tex]
2) Given : [tex]x^2+24=0[/tex]
To find : What is the solution of the equation when solved over the complex numbers?
Solution :
Quadratic equation, [tex]x^2+24=0[/tex]
Subtract 24 both side,
[tex]x^2+24-24=-24[/tex]
[tex]x^2=-24[/tex]
Taking root both side,
[tex]x=\sqrt{-24}[/tex]
[tex]x=\pm 2\sqrt{6}i[/tex]
The solution of the equation is [tex]x=2\sqrt{6}i,-2\sqrt{6}i[/tex]
