Quadratic Equations
Conjugate Roots
JEE Main
Grade 11
Question:
If $2 + i\sqrt{3}$ is a root of $x^2 + px + q = 0$ where $p, q$ are real, then $(p, q)$ equals:
(1) $(-4, 7)$
(2) $(4, -7)$
(3) $(-7, 4)$
(4) $(4, 7)$
Step-by-Step Solution
Key Concept: Complex roots of real-coefficient polynomials come in conjugate pairs. The other root is $2 - i\sqrt{3}$. Use Vieta to read off $p$ and $q$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)