Quadratic Equations
Roots Transformation
JEE Advanced
Grade 11
Question:
If $\alpha$ is a root of $2x(2x + 1) = 1$, then the other root is:
(1) $3\alpha^3 + 4\alpha$
(2) $\alpha^2$
(3) $-2\alpha(\alpha + 1)$
(4) None of these
Step-by-Step Solution
Key Concept: Rewrite the equation as $4x^2 + 2x - 1 = 0$. If $\alpha, \beta$ are the roots, then $\alpha + \beta = -1/2$. Express $\beta$ in terms of $\alpha$ using Vieta and the fact that $\alpha(2\alpha + 1) = 1/2$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)