ANSWER
[tex]x\text{ = }\frac{2}{3}\text{ + i}\frac{\sqrt[]{2}}{3}\text{and x = }\frac{2}{3}-\text{ i}\frac{\sqrt[]{2}}{3}[/tex]
EXPLANATION
A quadratic function is generally given as:
[tex]f(x)=ax^2\text{ + bx + c}[/tex]
The quadratic formula used to find the roots of a quadratic equation(function) is:
[tex]x\text{ = }\frac{-b\text{ }\pm\text{ }\sqrt[]{b^2\text{ - 4ac}}}{2a}[/tex]
From the function given, we have that:
a = 3, b = -4, c = 2
Therefore, the roots of the function are:
[tex]\begin{gathered} x\text{ = }\frac{-(-4)\text{ }\pm\sqrt[]{(-4)^2\text{ - 4(3)(2)}}}{2(3)} \\ x\text{ = }\frac{4\pm\sqrt[]{16\text{ - }24}}{6} \\ x\text{ = }\frac{4\text{ }\pm\sqrt[]{-8}}{6} \\ x\text{ = }\frac{2\text{ + 2 }\sqrt[]{-2}}{3}\text{ and x = }\frac{2\text{ - 2 }\sqrt[]{-2}}{3} \\ x\text{ = }\frac{2}{3}\text{ + i}\frac{\sqrt[]{2}}{3}\text{and x = }\frac{2}{3}-\text{ i}\frac{\sqrt[]{2}}{3} \end{gathered}[/tex]
