Q.

The number of values of a for which equations x3+ax+1=0 and x4+ax2+1=0 have a common root is

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a

0

b

1

c

2

d

infinite

answer is B.

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Detailed Solution

Given equations arex3+ax+1=0or x4+ax2+x=0              (1)and x4+ax2+1=0               (2)From (1) - (2), we get x - I. Thus, x = 1 is the common root.Hence,1+a+1=0⇒a=−2
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The number of values of a for which equations x3+ax+1=0 and x4+ax2+1=0 have a common root is