Q. If $\alpha$ and $\beta$ are the roots of the equation $x^{2} - 6x + a = 0$ and satisfy the relation $3\alpha + 2\beta = 16$, then the value of $a$ is
A) -8
B) 8
C) -16
D) 9
Explanation
(b)
Given relation is
$3\alpha + 2\beta = 16\ \Rightarrow 2(\alpha + \beta) + \alpha = 16$
$\Rightarrow 2 \times 6 + \alpha = 16\ \Rightarrow \ \alpha = 4\ \ \lbrack\because\ \alpha + \beta = 6,\ \alpha\beta = a\rbrack$
$\therefore\ \alpha^{2} - 6\alpha + a = 0$
$\Rightarrow 16 - 24 + a = 0\ \Rightarrow a = 8$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.