Quadratic Equations
Irrational Roots
Grade 11
Question:
<p>One root of the equation $x^4 - 5x^3 + ax^2 + bx + c = 0$ is $3 + \sqrt{...}$. If all the roots of the equation are real given that $a, b, c$ are rational parameters, then the greatest value of 'a' is equal to</p>
<p>(A) [Option not fully visible]</p>
<p>(B) [Option not fully visible]</p>
<p>(C) $2$</p>
<p>(D) [Option not fully visible]</p>
Step-by-Step Solution
Key Concept: If a polynomial with rational coefficients has an irrational root of form $p + \sqrt{q}$, its conjugate $p - \sqrt{q}$ must also be a root.
<p>Solution not provided in source text.</p>
Correct Answer: C