Multiple choice

The quadratic equation $ax^2+bx+c=0$ will have real and distinct roots if :

  1. $b^2-4ac < 0$
  2. $b^2-4ac > 0$
  3. $b^2-4ac = 0$

  4. All the above
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B Correct answer
Explanation

A quadratic equation ax^2 + bx + c = 0 has real and distinct roots if the discriminant D = b^2 - 4ac is greater than 0.

AI explanation

The discriminant of a quadratic equation ax^2 + bx + c = 0 is given by the expression b^2 - 4ac. The nature of the roots is determined entirely by the value of this discriminant. For a quadratic equation to have real and distinct roots, the discriminant must be strictly greater than zero. Therefore, the required condition is b^2 - 4ac > 0.

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