Quadratic Equations
Symmetric Expressions
JEE Main 2022
Grade 11
Question:
If $\alpha, \beta$ are the roots of $x^2 - 2x - 1 = 0$, then the value of $\alpha^2\beta + \alpha\beta^2$ is:
(1) $-4$
(2) $-2$
(3) $2$
(4) $4$
Step-by-Step Solution
Key Concept: Factor: $\alpha^2\beta + \alpha\beta^2 = \alpha\beta(\alpha + \beta)$. Read $\alpha + \beta$ and $\alpha\beta$ from Vieta's formulas.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)