Respuesta :
ANSWER
[tex]x\text{ = 0.167 + }1.142i\text{ and x = 0.167 }-\text{ 1.142i}[/tex]EXPLANATION
We want to find the solutions of the equation.
The solutions of the equation are the values of x that make that equation equal to zero (0).
The equation given is:
[tex]3x^2\text{ - x + 4}[/tex]We need to use the quadratic formula.
For a quadratic equation:
[tex]ax^2\text{ + bx + c}[/tex]the quadratic formula is:
[tex]x\text{ = }\frac{-b\text{ }\pm\text{ }\sqrt[]{b^2\text{ - 4ac}}}{2a}[/tex]So, we have that:
a = 3, b = -1, c = 4
So::
[tex]\begin{gathered} x\text{ = }\frac{-(-1)\text{ }\pm\sqrt[]{(-1)^2_{}-\text{ 4(3)(4)}}}{2(3)}\text{ = }\frac{1\text{ }\pm\text{ }\sqrt[]{1\text{ - 48}}}{6} \\ x=\text{ }\frac{1\text{ }\pm\text{ }\sqrt[]{-47}}{6}\text{ = }\frac{1\text{ }\pm\text{ }\sqrt[]{47}\cdot\text{ }\sqrt[]{-1}}{6}\text{ = }\frac{1\text{ }\pm\text{ }\sqrt[]{47}\text{ i}}{6} \\ x\text{ = }\frac{1\text{ + 6.86i}}{6}\text{ and x = }\frac{1\text{ - 6.86i}}{6} \\ x\text{ = 0.167 + }1.142i\text{ and x = 0.167 }-\text{ 1.142i} \end{gathered}[/tex]The equation has complex solutions.
