Q. If one root of the equation $x^{2} + px + q = 0$ is $2 + \sqrt{3}$, then the value of the $p$ and $q$ respectively
A) $- 4,\ 1$
B) $4,\ - 1$
C) $2,\ \sqrt{3}$
D) $- 2,\ - \sqrt{3}$
Explanation
(a)
Since, one root of the equation
$x^{2} + px + q = 0$ is $2 + \sqrt{3}$, then the other root will be
$2 - \sqrt{3}$
$\therefore$ Since of roots $2 + \sqrt{3} + 2 - \sqrt{3} = - p$
$\Rightarrow p = - 4$
And product of roots
$\left( 2 + \sqrt{3} \right)\left( 2 - \sqrt{3} \right) = q$
$\Rightarrow q = 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.