Multiple choice

The equation (x2 + 1)2 - x2 = 0 has

  1. four real roots

  2. two real roots

  3. no real root

  4. one real root

  5. cannot be determined
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Expanding (x^2 + 1)^2 - x^2 = 0 gives x^4 + 2x^2 + 1 - x^2 = 0, which simplifies to x^4 + x^2 + 1 = 0. Since x^4 and x^2 are always non-negative for real x, x^4 + x^2 + 1 is at least 1, meaning there are no real roots.

AI explanation

Expand the binomial to rewrite the equation as x4 + 2x2 + 1 - x2 = 0, which simplifies to x4 + x2 + 1 = 0. This is a quadratic equation in terms of x2, where the discriminant is calculated as 1 squared minus 4 times 1 times 1, resulting in negative 3. Since the discriminant is negative, there are no real values for x2, meaning the equation has no real roots.

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