Multiple choice

The roots of the equations $\displaystyle x^{2}-x-3=0$ are

  1. Imaginary

  2. Rational

  3. Irrational

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The discriminant of x^2 - x - 3 = 0 is D = (-1)^2 - 4(1)(-3) = 1 + 12 = 13. Since 13 is not a perfect square, the roots are real and irrational.

AI explanation

The discriminant is b^2 - 4ac. Substituting a=1, b=-1, and c=-3 gives (-1)^2 - 4(1)(-3) = 13. Since 13 is positive but not a perfect square, the roots are real and irrational.

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