Question

If $x^3+ax+1=0$ and $x^4+a{x}^2+1=0$ have a common root, then $a$ is equal to:

• A. $-2$
• B. $2$
• C. $-1$
• D. $1$

Answer 1

The correct option is A

$-2$

$x^3+ax+1=0$ and $x^4+a{x}^2+1=0$ have a common root.
$(x^4+a{x}^2+x)-(x^4+a{x}^2+1)=0$

$x=1$ is the common root.

$x^3+ax+1=0$
$\Rightarrow 1+a+1=0\Rightarrow a=-2$