Question

If the roots of the quadratic equation \( ax^2 + bx + c = 0 \) are real and distinct, what is the condition on the discriminant?

• A. \( b^2 - 4ac>0 \)
• B. \( b^2 - 4ac = 0 \)
• C. \( b^2 - 4ac<0 \)
• D. None of the above

Hint:

To determine the nature of the roots, always check the discriminant (\( \Delta \)): if \( \Delta>0 \), the roots are real and distinct.

Answer 1

The Correct Option is A

The discriminant of a quadratic equation \( ax^2 + bx + c = 0 \) is given by: \[ \Delta = b^2 - 4ac \] For the roots to be real and distinct, the discriminant must be positive. Thus, the condition for real and distinct roots is: \[ \Delta = b^2 - 4ac>0 \] Therefore, the correct answer is: \[ \boxed{(A) \, b^2 - 4ac>0} \]