Quadratic Equations
Symmetric Expressions
JEE Main
Grade 11
Question:
If $\alpha, \beta$ are the roots of $x^2 - 2x + 3 = 0$, then $\alpha^3 + \beta^3$ equals:
(1) $2$
(2) $8$
(3) $-10$
(4) $-2$
Step-by-Step Solution
Key Concept: Use $\alpha^3 + \beta^3 = (\alpha + \beta)^3 - 3\alpha\beta(\alpha + \beta)$. Read $\alpha + \beta = 2$ and $\alpha\beta = 3$ from Vieta, then substitute.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)