Multiple choice

If the roots of equation x2 + ax + 1 = 0 are imaginary, in which of the following intervals does the value of a lie?

  1. (- 2, - 1)

  2. (- 2, - 2)

  3. (- 2, 2)

  4. (- 2, 1)

  5. (- 1, 2)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For roots to be imaginary, the discriminant D = b^2 - 4ac must be less than 0. Here, a^2 - 4(1)(1) < 0, so a^2 < 4, which means -2 < a < 2.

AI explanation

For the quadratic equation x^2 + ax + 1 = 0, the condition for imaginary roots is that the discriminant must be less than zero. The discriminant is (a^2 - 4), so setting a^2 - 4 < 0 gives a^2 < 4. Taking the square root gives the interval for a as (-2, 2). The value of a lies in the interval (-2, 2).

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