<p>Lines must be parallel. If <em>p(p<sup>2</sup> + 1) = −(p<sup>2</sup> + 1)</em>, then the value of <em>p</em> is:</p>
Step-by-Step Solution
Key Concept: Rearrange the equation to factor out the common term (p² + 1), recognizing that p² + 1 is always positive for real p, allowing us to divide both sides by it to solve for p.
<p><strong>Step 1:</strong> Start with the equation p(p² + 1) = -(p² + 1)</p><p><strong>Step 2:</strong> Rearrange by moving all terms to one side: p(p² + 1) + (p² + 1) = 0</p><p><strong>Step 3:</strong> Factor out the common term (p² + 1): (p² + 1)(p + 1) = 0</p><p><strong>Step 4:</strong> Since p² + 1 > 0 for all real values of p (always positive), we cannot have p² + 1 = 0</p><p><strong>Step 5:</strong> Therefore, p + 1 = 0, which gives p = -1</p><p>∴ Answer: B (p = -1)</p>
Correct Answer: B