[tex]ax^2+bx+c=0[/tex]
Quadratic Formula: [tex]x = \frac{-b\pm \sqrt{b^2-4ac} }{2a} [/tex]
1) a = 3 ; b = -9 ; c = 27
[tex]x = \frac{9\pm \sqrt{81-4(3)(27)} }{2(3)}[/tex]
[tex]x = \frac{9\pm \sqrt{-243} }{6}[/tex]
[tex]x = \frac{9\pm 9\sqrt{-3} }{6}= \frac{3\pm 3\sqrt{-3} }{2}[/tex]
[tex]\boxed{x_1= \frac{3+ 3\sqrt{-3} }{2}= \frac{3+ 3i\sqrt{3} }{2}}[/tex]
[tex]\boxed{x_2= \frac{3- 3\sqrt{-3} }{2}= \frac{3-3i\sqrt{3} }{2}}[/tex]
2) a = 2 ; b = 10 ; c = -4
[tex]x = \frac{-10\pm \sqrt{100-4(2)(-4)} }{2(2)}[/tex]
[tex]x = \frac{-10\pm \sqrt{132} }{4}[/tex]
[tex]x = \frac{-10\pm 2\sqrt{33} }{4}=\frac{-5\pm\sqrt{33} }{2}[/tex]
[tex]\boxed{x_1= \frac{-5+\sqrt{33} }{2}}[/tex]
[tex]\boxed{x_2= \frac{-5-\sqrt{33} }{2}}[/tex]
3) a = 4 ; b = -8 ; c = 3
[tex]x = \frac{8\pm \sqrt{64-4(4)(3)} }{2(4)}[/tex]
[tex]x = \frac{8\pm \sqrt{16} }{8}[/tex]
[tex]x = \frac{8\pm4 }{8}=\frac{2\pm1 }{2}[/tex]
[tex]x_1 =\frac{2+1 }{2}=\boxed{\frac{3}{2}}[/tex]
[tex]x_2 =\frac{2-1 }{2}=\boxed{\frac{1}{2}}[/tex]
