Multiple choice

The roots of quadratic equation 2x2 + x + 4 = 0 are:

  1. Positive and negative

  2. Both Positive

  3. Both Negative

  4. No real roots
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The discriminant D = b^2 - 4ac = (1)^2 - 4(2)(4) = 1 - 32 = -31. Since the discriminant is negative, the equation has no real roots.

AI explanation

To determine the nature of the roots, we calculate the discriminant using the formula D = b^2 - 4ac for the equation 2x^2 + x + 4 = 0. Substituting a = 2, b = 1, and c = 4 gives D = 1^2 - 4(2)(4) = 1 - 32 = -31. Because the discriminant is less than zero, the quadratic equation has no real roots.

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