Multiple choice

If the roots of a quadratic expression $ax^2+bx+c$ are complex, then

  1. $b^2 <4ac$
  2. $b^2 >4ac$
  3. $b^2 =4ac$
  4. $a=0$
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A Correct answer
Explanation

For a quadratic equation ax^2 + bx + c = 0, the roots are complex if the discriminant D = b^2 - 4ac is less than 0. Therefore, b^2 < 4ac.

AI explanation

The nature of the roots for a quadratic expression ax^2 + bx + c is determined by its discriminant, D = b^2 - 4ac. If the roots are complex or imaginary, the discriminant must be less than zero. Therefore, the condition for complex roots is b^2 < 4ac.

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