Question

Number of values of $a$ for which equations $x^3+ax+1=0$ and $x^4+a{x}^2+1=0$ have a common root

• A. $0$
• B. $1$
• C. $2$
• D. $\infty$

Answer 1

The correct option is B $1$

$x^3+ax+1=0\to \left(1\right)x^4+a{x}^2+1=0\to \left(2\right)\left(1\right)-\left(2\right)x^3-x^4+ax-a{x}^2=0$

we get $x=1$. Thus $x=1$ is common root.

$\therefore x^3+ax+1=0$

$⟹1+a+1=0$

$\therefore a=-2$

so only one value of $a$.