The number of values of `a` for which equations `x^3+a x+1=0 and x^4+a x^2+1=0` have a common root is

Options

A. 0
B. 1
C. 2
D. infinite

Answer

B

Explanation

Given equation are
`x^(3) + ax + 1 = 0`
or `x^(4) + ax^(2) + x = 0 " "(1)`
and `x^(4) + ax^(2) + 1 = 0" "(2)`
From (1) - (2), we get x = 1. Thus, x = 1 is the common root Hence,
`1 + a + 1 = 0 rArr a = -2`