Answer:
[tex]x=\dfrac{-3\pm \sqrt7i}{2}[/tex]
Step-by-step explanation:
The given equation is [tex]x^{2}+3x+4=0[/tex].
We need to find the solution of the above equation.
The solution of an equation [tex]ax^2+bx+c=0[/tex] is :
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]
We have, a = 1, b = 3 and c = 4
[tex]x=\dfrac{-3+ \sqrt{(3)^2-4(1)(4)} }{2}, \dfrac{-3- \sqrt{(3)^2-4(1)(4)} }{2}\\\\=\dfrac{-3+\sqrt{9-16}}{2}, \dfrac{-3-\sqrt{9-16}}{2}\\\\=\dfrac{-3\pm \sqrt7i}{2}[/tex]
So, the solution of the given equation is [tex]\dfrac{-3\pm \sqrt7i}{2}[/tex].
