Multiple choice

How many positive roots does the equation x6 + x4 + x2 + 1 = 0 have?

  1. None

  2. 1

  3. 2

  4. 4
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Since x^6, x^4, and x^2 are all non-negative for any real x, x^6 + x^4 + x^2 + 1 is always >= 1. Thus, it can never be zero for any real x.

AI explanation

Because x is raised to even powers (6, 4, 2), any real value substituted for x will yield a positive term or 1, ensuring the total sum is strictly greater than zero. A positive integer input makes the expression greater than 1, while a negative integer input also yields a positive result; thus, the equation can never equal zero. Therefore, there are no positive roots.

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