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 the equation ax² + bx + c = 0, sum of roots (α+β) = -b/a, product (αβ) = c/a. Here, a=3, b=4, c=-5. So α+β = -4/3, αβ = -5/3. Then α² + β² = (α+β)² - 2αβ = (-4/3)² - 2(-5/3) = 16/9 + 10/3 = 16/9 + 30/9 = 46/9.
Hint
Use the relationships: α² + β² = (α+β)² - 2αβ.