Multiple choice

The equation $x+\dfrac {1}{x}=2x^2$ has a root $1$. Then it will have

  1. no other root

  2. one more root only

  3. two more roots
  4. another root $-1$
Reveal answer Fill a bubble to check yourself
C Correct answer
AI explanation

Multiplying the equation x + 1/x = 2x^2 by x clears the denominator and yields the cubic equation 2x^3 - x - 1 = 0. Because the original equation has a root at 1, we can factor out (x - 1) from the cubic polynomial, leaving the quadratic factor 2x^2 + 2x + 1. Setting this quadratic factor to zero reveals two additional complex roots, proving the equation has exactly two more roots.

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