Question Detail
Question
Given that \(\alpha\) and \(\beta\) are the roots of the quadratic equation \(3x^2 + 4x - 5 = 0\), Find the value of \(\alpha^2 + \beta^2\).
Correct Answer
Option A is the correct answer.
Detailed Explanation
For (3x^2 + 4x - 5 = 0), sum (\alpha + \beta = -\frac{4}{3}), product (\alpha\beta = -\frac{5}{3}). Then (\alpha^2 + \beta^2 = (\alpha+\beta)^2 - 2\alpha\beta = \left(-\frac{4}{3}\right)^2 - 2\left(-\frac{5}{3}\right) = \frac{16}{9} + \frac{10}{3} = \frac{16}{9} + \frac{30}{9} = \frac{46}{9}).
Hint
Use \(\alpha^2 + \beta^2 = (\alpha+\beta)^2 - 2\alpha\beta\).