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The value of $a$ for which the equations $x^3+a x+1=0$ and $x^4+a x^2+1=0$ have a common root is
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Verified Answer
The correct answer is:
-2
Let $a=-2$,
$\therefore x^3-2 x+1=0 \text { and } x^4-2 x^2+1=0$
Put $x=1$, we get
$\begin{array}{rlrl}
\Rightarrow & 1-2+1 & =0 \text { and } 1-2+1=0 \\
0 =0 \text { and } 0=0
\end{array}$
Hence, required value is $a=-2$
$\therefore x^3-2 x+1=0 \text { and } x^4-2 x^2+1=0$
Put $x=1$, we get
$\begin{array}{rlrl}
\Rightarrow & 1-2+1 & =0 \text { and } 1-2+1=0 \\
0 =0 \text { and } 0=0
\end{array}$
Hence, required value is $a=-2$
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