Question

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

• A. -2
• B. -1
• C. 1
• D. 2

Answer 1

The correct option is A -2

$x^3+ax+1=0$.........(1)

and $x^4+a{x}^2+1=0$ .......(2)

Now (2)$-x\cdot$(1)

$\Rightarrow a{x}^2+1-a{x}^2-x=0$

$\Rightarrow x=1$, so $x=1$ is the common root

Hence $1+a+1=0\Rightarrow a=-2$