Multiple choice

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

  1. $b^2-4ac=0$
  2. $b^2-4ac\ge0$
  3. $b^2-4ac<0$
  4. $b^2-4ac>0$
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A Correct answer
Explanation

For a quadratic equation ax^2 + bx + c = 0, the nature of the roots is determined by the discriminant, D = b^2 - 4ac. When the roots are real and equal, the discriminant must be exactly equal to zero. Thus, b^2 - 4ac = 0 is the correct condition.

AI explanation

The discriminant of the quadratic equation ax^2+bx+c=0 determines the nature of its roots. For roots to be real and equal, the discriminant must equal zero. Therefore, b^2-4ac=0 is the correct condition.

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