Respuesta :
Given equation is [tex]3x^2 + 3x + 4 = 0[/tex]
Now we can compare it with general form of quadratic equation ([tex]ax^2 + bx + c = 0[/tex])
a = 3 , b = 3 and c = 4
Now we can apply quadratic formula which is given as
[tex]x =\frac{ -b+/- \sqrt{b^2-4ac} }{2a}[/tex]
Now we can plugin value of a , b or c
[tex]x = \frac{-3+/- \sqrt{(3)^2 - 4*3*4} }{2*3} [/tex]
[tex]= \frac{-3+/- \sqrt{9 - 48} }{6} = \frac{-3+/- \sqrt{-39} }{6} [/tex]
In general we know [tex] \sqrt{-1} = i [/tex]
So we can write [tex] \sqrt{-39 } = \sqrt{-1} * \sqrt{39} = i \sqrt{39} [/tex]
So
[tex]x = \frac{-3+/-i \sqrt{39} }{6} [/tex]
So [tex]x = \frac{-3+i \sqrt{39} }{6} [/tex] or [tex]x = \frac{-3- \sqrt{39} }{6} [/tex]
Now we can compare it with general form of quadratic equation ([tex]ax^2 + bx + c = 0[/tex])
a = 3 , b = 3 and c = 4
Now we can apply quadratic formula which is given as
[tex]x =\frac{ -b+/- \sqrt{b^2-4ac} }{2a}[/tex]
Now we can plugin value of a , b or c
[tex]x = \frac{-3+/- \sqrt{(3)^2 - 4*3*4} }{2*3} [/tex]
[tex]= \frac{-3+/- \sqrt{9 - 48} }{6} = \frac{-3+/- \sqrt{-39} }{6} [/tex]
In general we know [tex] \sqrt{-1} = i [/tex]
So we can write [tex] \sqrt{-39 } = \sqrt{-1} * \sqrt{39} = i \sqrt{39} [/tex]
So
[tex]x = \frac{-3+/-i \sqrt{39} }{6} [/tex]
So [tex]x = \frac{-3+i \sqrt{39} }{6} [/tex] or [tex]x = \frac{-3- \sqrt{39} }{6} [/tex]
