Question

The roots of the quadratic equation \(x^2 + x – p (p + 1) = 0 \)are :

• A. p, p + 1
• B. – p, p + 1
• C. – p, – (p + 1)
• D. p, – ( p + 1)

Answer 1

The Correct Option is D

The roots of a quadratic equation $ax^2 + bx + c = 0$ are given by:
\[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.\]
Here, $a = 1$, $b = 1$, and $c = -p(p + 1)$. Substituting:
\[x = \frac{-1 \pm \sqrt{1 + 4p(p + 1)}}{2}.\]
This simplifies to:
\[x = -p, \quad x = -(p + 1).\]