Value of a for which equations x 3 + a x + 1 = 0 and x 4 + a x 2 + 1 = 0 have a common root

Value of a for which equations x3+ax+1=0 and x4+ax2+1=0 have a common root
  1. 0
  2. 1
  3. -2
  4. none of these.

Solution

Given equations are

x3+ax+1=0

⇒x4+ax2+x=0   …1

And,

x4+ax2+1=0   …2

Subtracting equations 1 and 2, we get

x-1=0

⇒x=1

Thus, x=1 is the common root. Hence,

1+a+1=0

⇒a=-2

Asked in: AP EAMCET 2021 (19 Aug Shift 2)

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