Quadratic Equations
Relations Between Roots and Coefficients
JEE Main
Grade 11
Question:
If one root of $5x^2 + 13x + k = 0$ is the reciprocal of the other, then $k$ equals:
(1) $1$
(2) $3$
(3) $5$
(4) $7$
Step-by-Step Solution
Key Concept: If the roots are $\alpha$ and $1/\alpha$, then their product $= 1$. Use Vieta's formula for the product of roots.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)