Multiple choice

The roots of the equation $x^2 + x = 2(x - 1)$ are

  1. imaginary

  2. rational

  3. irrational

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

x^2 + x = 2x - 2 => x^2 - x + 2 = 0. Discriminant D = b^2 - 4ac = (-1)^2 - 4(1)(2) = 1 - 8 = -7. Since D < 0, the roots are imaginary.

AI explanation

Simplifying the equation x squared plus x equals the quantity x minus one gives x squared plus x equals two x minus two. Rearranging all terms to one side yields x squared minus x plus two equals zero. The discriminant is b squared minus four times a times c, which equals one minus eight, giving negative seven; since the discriminant is negative, the roots are imaginary.

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