If the two real roots are distinct, then which of the following may be correct?

Options

A. Both are negative
B. One is positive and another one is. negative
C. Both are positive
D. all of the above

Answer

To determine which of the given options may be correct when two real roots are distinct, we can analyze the nature of the roots of a quadratic equation. Let's denote the quadratic equation as \( ax^2 + bx + c = 0 \). The roots of this equation can be found using the quadratic formula:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

### Step 1: Identify the Condition for Distinct Real Roots
For the roots to be distinct and real, the discriminant \( D \) must be greater than zero:

\[ D = b^2 - 4ac > 0 \]