Question

The non-integer roots of \( x^4 - 3x^3 - 2x^2 + 3x + 1 = 0 \) are:

• A. \( \frac{1}{3} \pm \sqrt{3} \)
• B. \( \frac{3}{4} \pm \sqrt{3} \)
• C. \( \frac{1}{3} \pm \sqrt{5} \)
• D. \( \frac{1}{2} \pm \sqrt{5} \)

Hint:

For higher degree polynomials, use factorization, synthetic division, or numerical methods to find the roots.

Answer 1

The Correct Option is A

Step 1: Finding roots of the equation. Use the quadratic or factorization method to find the roots of the quartic equation. The non-integer roots are found to be \( \frac{1}{3} \pm \sqrt{3} \).
Step 2: Conclusion. Thus, the non-integer roots of the equation are \( \frac{1}{3} \pm \sqrt{3} \).