Answer: \(x^2 - \frac{1}{4} = 0 \text{, i.e. } 4x^2 - 1 = 0\)
Required equation: \(x^2 - (\alpha + \beta)x + \alpha\beta = 0\).
Sum \(= \frac{1}{2} - \frac{1}{2} = 0\)
Product \(= \frac{1}{2}\times\left(-\frac{1}{2}\right) = -\frac{1}{4}\)
So the equation is \(x^2 - \frac{1}{4} = 0 \text{, i.e. } 4x^2 - 1 = 0\).