Quadratic Equations
Relations Between Roots and Coefficients
JEE Main
Grade 11
Question:
If the roots of $x^2 + px + q = 0$ are $\tan 30^\circ$ and $\tan 15^\circ$, then $2 + q - p$ equals:
(1) $1$
(2) $3$
(3) $0$
(4) $2$
Step-by-Step Solution
Key Concept: Use $\tan(30^\circ + 15^\circ) = \tan 45^\circ = 1$ and the addition formula to relate $\tan 30^\circ + \tan 15^\circ$ and $\tan 30^\circ \cdot \tan 15^\circ$ (i.e. $-p$ and $q$).
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)