Multiple choice

The roots of the equation $ax^2 + bx + c = 0$ will be imaginary if

  1. $a > 0, b = 0, c < 0$
  2. $a > 0, b = 0, c > 0$
  3. $a = 0, b > 0, c > 0$
  4. $a > 0, b > 0, c = 0$
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B Correct answer
Explanation

Roots are imaginary if the discriminant D = b^2 - 4ac < 0. For a > 0 and c > 0, 4ac is positive, making b^2 - 4ac < 0 if b is 0.

AI explanation

The nature of the roots is determined by the discriminant, given by b squared minus four times a times c. If a is greater than zero, b is zero, and c is greater than zero, the discriminant becomes zero squared minus four times a positive number times a positive number, resulting in a negative value. Because the discriminant is strictly negative, the roots will be imaginary.