Question

The value of $a$ for which $x^3+ax+1=0$ and $x^4+a{x}^2+1=0$ have exactly one common root is

• A. $-3$
• B. $0$
• C. $-1$
• D. $-2$

Answer 1

The correct option is D $-2$

$x^3+ax+1=0\cdots \left(1\right)x^4+a{x}^2+1=0\cdots \left(2\right)$
Subtracting $x\times \left(1\right)$ from $\left(2\right)$, we get
$1-x=0\Rightarrow x=1$
Putting $x=1$ in equation $\left(1\right)$, we get
$1+a+1=0\Rightarrow a=-2$