Final answer:
To solve the equation αx² + 2α²x + 1 = 0, we can use the quadratic formula. The solutions for x are (-α + 2√(α⁴ - α)) / α and (-α - 2√(α⁴ - α)) / α
Step-by-step explanation:
To solve the equation αx² + 2α²x + 1 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b² - 4ac)) / (2a)
In our equation, a = α, b = 2α², and c = 1. Substituting these values into the quadratic formula, we get:
x = (-2α² ± √((2α²)² - 4α(1))) / (2α)
This can be simplified further:
x = (-α ± √(4α⁴ - 4α)) / α
x = (-α ± 2√(α⁴ - α)) / α