Multiple choice

If the roots of the quadratic equation $ax^2+bx+c=0$ are all imaginary then which one of the following is true

  1. $b^2-4ac\ge 0$
  2. $b^2-4ac<0$
  3. $b^2-4ac=0$
  4. $b^2-4ac>0$
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B Correct answer
Explanation

For a quadratic equation ax^2 + bx + c = 0, the roots are imaginary if and only if the discriminant b^2 - 4ac is less than zero.

AI explanation

The discriminant of a quadratic equation ax^2 + bx + c = 0 is given by the formula D = b^2 - 4ac. If the roots are imaginary, the value under the square root in the quadratic formula must be negative. Therefore, the condition that must be true is b^2 - 4ac < 0.

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