Quadratic Equations
Relations Between Roots and Coefficients
JEE Main
Grade 11
Question:
If the sum of roots of $x^2 - (k + 6)x + 2(2k - 1) = 0$ equals half the product of roots, then $k$ equals:
(1) $3$
(2) $5$
(3) $9$
(4) $7$
Step-by-Step Solution
Key Concept: Write: sum $= k + 6$ and product $= 2(2k - 1)$. Set sum $= \frac{1}{2} \times$ product and solve for $k$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (4)