Quadratic Equations
Polynomial Roots
Grade 11
Question:
<p>Let \(p(x) = x^6 + ax^5 + bx^4 + x^3 + bx^2 + ax + 1\). Given that 1 is a root of \(p(x) = 0\) and –1 is not. What is the maximum number of distinct real roots that \(p\) could have</p>
<p>(A) 6</p>
<p>(B) 5</p>
<p>(C) 4</p>
<p>(D) 3</p>
Step-by-Step Solution
Key Concept: Observe that \(p(x)\) has palindromic structure. If \(r\) is a root, then \(1/r\) is also a root. Use \(p(1) = 0\) to find constraint and determine maximum real roots.
<p>Solution not provided in text.</p>
Correct Answer: B