Multiple choice

In the following, determine whether the given quadratic equations have real roots and if so, find the roots : $x^2$ + x + 2 = 0

  1. $real, -1,0$
  2. $real, -1,1$
  3. $real, 1,0$
  4. $\text{not real}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For x^2 + x + 2 = 0, the discriminant D = b^2 - 4ac = 1^2 - 4(1)(2) = 1 - 8 = -7. Since D < 0, the roots are not real.

AI explanation

To determine the nature of the roots for x^2 + x + 2 = 0, we calculate the discriminant using the formula b squared minus 4ac. Here, a is 1, b is 1, and c is 2, so the discriminant is 1 squared minus 4 times 1 times 2, resulting in 1 minus 8, which equals negative 7. Since the discriminant is less than zero, the quadratic equation does not have real roots. The result is not real.

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