Multiple choice

The number of values of $a$ for which equation $x^3+ax+1=0$ and $x^4+ax^2+1=0$ have a common root, is:

  1. $0$
  2. $1$
  3. $2$
  4. $\infty$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If x is a common root, x^3 + ax + 1 = 0 and x^4 + ax^2 + 1 = 0. Multiply the first by x: x^4 + ax^2 + x = 0. Subtracting the second equation: (x^4 + ax^2 + x) - (x^4 + ax^2 + 1) = 0 => x - 1 = 0, so x = 1. Substituting x = 1 into the first equation: 1 + a + 1 = 0, so a = -2. There is only one value for a.

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