Quadratic Equations
Common Roots
JEE Main
Grade 11
Question:
If $x^2 + ax + b = 0$ and $x^2 + bx + a = 0$ ($a \neq b$) have a common root, then $a + b$ equals:
(1) $1$
(2) $-1$
(3) $0$
(4) $2$
Step-by-Step Solution
Key Concept: Subtract the two equations to find the common root $\alpha$ directly. Substitute back into either equation to find the relation between $a$ and $b$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)