Question

Determine the sum of the roots of the quadratic equation 3X squared - 4X + 4 = 0

Answer 1

4/3

Step-by-step explanation:

If we have an equation with the form:

ax² + bx + c = 0

where a, b, and c are constants, we can calculate the roots of the equation, using the following:

`\begin{gathered} x=\frac{-b+\sqrt[]{b^2-4ac}}{2a} \\ \text{and} \\ x=\frac{-b-\sqrt[]{b^2-4ac}}{2a} \end{gathered}`

In this case, the equation is: 3x² - 4x + 4

So, a is 3, b is -4 and c is 4. Therefore, the roots of the equation are:

`\begin{gathered} x=\frac{-(-4)+\sqrt[]{(-4)^2-4\cdot3\cdot4}}{2\cdot3}=\frac{4+\sqrt[]{16-48}}{6}=\frac{4+\sqrt[]{-32}}{6} \\ x=\frac{-(-4)-\sqrt[]{(-4)^2-4\cdot3\cdot4}}{2\cdot3}=\frac{4-\sqrt[]{16-48}}{6}=\frac{4-\sqrt[]{-32}}{6} \end{gathered}`

Therefore, the sum of the roots is equal to:

`\frac{4+\sqrt[]{-32}}{6}+\frac{4-\sqrt[]{-32}}{6}=\frac{4+\sqrt[]{-32}+4-\sqrt[]{-32}}{6}=(8)/(6)=(4)/(3)`

So, the answer is 4/3