Multiple choice

Which of the following conditions is satisfied if the quadratic equation ax2 + bx + c = 0 has no real roots?

  1. b2 - 4ac < 0

  2. b2 - 2ac > 0

  3. b2 - 4ac = 0

  4. b2 - 4ac > 0
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A Correct answer
Explanation

For a quadratic equation ax^2 + bx + c = 0 to have no real roots, the discriminant D = b^2 - 4ac must be less than 0.

AI explanation

A quadratic equation ax^2 + bx + c = 0 has no real roots when its discriminant is strictly negative. The formula for the discriminant is D = b^2 - 4ac. Therefore, setting b^2 - 4ac < 0 ensures the equation has no real roots.

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