Q. The value of $a$ for which the equations $x^{3} + ax + 1 = 0\ and\ x^{4} + ax^{2} + 1 = 0$ have a common root, is
A) $- 2$
B) $- 1$
C) 1
D) 2
Explanation
(a)
On multiplying first equation by $x$, we get
$x^{4} + ax^{2} + x = 0$ ….(i)
and another given equation is
$x^{4} + ax^{2} + 1 = 0$ ….(ii)
On subtracting Eq. (ii) from Eq. (i), we get
$x - 1 = 0\ \Rightarrow x = 1$
Which is a common root.
On putting this value in Eq. (ii), we get
$1 + a + 1 = 0$
$\Rightarrow a = - 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.