Question

What is the answer to this equation using the quadratic formula?
3x^2+2x+4x=0

Answer 1

`~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{3}x^2\stackrel{\stackrel{b}{\downarrow }}{+2}x\stackrel{\stackrel{c}{\downarrow }}{+4}=0 \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x= \cfrac{ - (2) \pm \sqrt { (2)^2 -4(3)(4)}}{2(3)}\implies x=\cfrac{-2\pm √(4-48)}{6}`

`x=\cfrac{-2\pm √(-44)}{6}\implies x=\cfrac{-2\pm √((-1)(2^2)(11))}{6}\implies x=\cfrac{-2\pm 2~i√(11)}{6} \\\\\\ x=\cfrac{2(-1\pm i√(11))}{6}\implies x=\cfrac{-1\pm i √(11)}{3}`

mind you that it has two complex roots, or imaginary values.