Question

If the roots of the equation \( x^2 + 2bx + c = 0 \) are \( \alpha \) and \( \beta \), then \( b^2 - c = \)

• A. \( \frac{(\alpha - \beta)^2}{4} \)
• B. \( (\alpha + \beta)^2 - \alpha\beta \)
• C. \( (\alpha + \beta)^2 + \alpha\beta \)
• D. \( \frac{(\alpha - \beta)^2}{2} + \alpha\beta \)
• E. \( \frac{(\alpha + \beta)^2}{2} + \alpha\beta \)

Hint:

For any quadratic $ax^2 + bx + c = 0$, the discriminant $\mathcal{D} = b^2 - 4ac$ is always equal to $a^2(\alpha - \beta)^2$.

Answer 1

The Correct Option is A