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The given equation is:

\[
f(x) = x^4 - 3x^3 - 5x^2 + 9x - 2 = 0
\]

It is mentioned that one of the roots is \( 2 + \sqrt{3} \).

### Step-by-Step Approach:
Since \( 2 + \sqrt{3} \) is a root of the polynomial and the coefficients of the polynomial are real, its conjugate \( 2 - \sqrt{3} \) must also be a root.

This suggests that the quadratic factor of the polynomial can be written as:

\[
(x - (2 + \sqrt{3}))(x - (2 - \sqrt{3})) = (x - 2)^2 - (\sqrt{3})^2 = x^2 -

Solve f(x) = x^4 - 3x^3 - 5x^2 + 9x - 2 = 0 with one root being 2 + √3.

This page covers how to solve the polynomial equation x^4 - 3x^3 - 5x^2 + 9x - 2 = 0, given one root is 2 + √3. Learn about polynomial division, factorization, and the conjugate root theorem. Suitable for Grades 11-12.

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