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

User Retrohacker
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1 Answer

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29 votes

ANSWER


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.

User Paddy
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