Question 16

If the equations $$x^3+ax+1=0$$ and $$x^4-ax^2+1=0$$ have a common root, then the value of $$a^2$$ is

Correct Answer: 0

Solution

Eliminating the common root gives the condition $$4a^4-4a^3+4a^2+7a+2=0$$, which does not determine one unique value of $$a^2$$. Therefore the problem has no single numerical answer and the source treats it as a bonus. The value $$0$$ is only a required placeholder.

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