To solve the quadratic equation \(3x^2 - 8x + 4 = 0\), we can use the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
We already identified the values of \(a\), \(b\), and \(c\):
- The value of \(a\) is \(3\).
- The value of \(b\) is \(-8\).
- The value of \(c\) is \(4\).
Substituting these values into the quadratic formula:
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Calculate the discriminant: \[ b^2 - 4ac = (-8)^2 - 4(3)(4) = 64 - 48 = 16 \]
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Substitute into the quadratic formula: \[ x = \frac{-(-8) \pm \sqrt{16}}{2(3)} \] \[ x = \frac{8 \pm 4}{6} \]
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Calculate the two possible solutions:
- First solution: \[ x = \frac{8 + 4}{6} = \frac{12}{6} = 2 \]
- Second solution: \[ x = \frac{8 - 4}{6} = \frac{4}{6} = \frac{2}{3} \approx 0.67 \]
Now, looking at the given response options for Question 3, the solutions would be:
- The solution \( (2, 0) \) corresponds to \(x = 2\).
- The solution \( (-0.67, 0) \) corresponds to \(x \approx 0.67\), which is not an exact match but is close.
Since \(2\) is one of the values we calculated from the equation, the answer to Question 3 is: (2, 0).