Question

What are the solutions of 3x^2 - x + 4 = 0

Answer 1

`x\text{ = 0.167 + }1.142i\text{ and x = 0.167 }-\text{ 1.142i}`

Step-by-step 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:

`3x^2\text{ - x + 4}`

We need to use the quadratic formula.

For a quadratic equation:

`ax^2\text{ + bx + c}`

the quadratic formula is:

`x\text{ = }\frac{-b\text{ }\pm\text{ }\sqrt[]{b^2\text{ - 4ac}}}{2a}`

So, we have that:

a = 3, b = -1, c = 4

So::

`\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}`

The equation has complex solutions.