The number of real roots of $x^4 - 4x^3 + 5x^2 - 4x + 1 = 0$ is:
Step-by-Step Solution
Key Concept: Divide through by $x^2$ and substitute $t = x + 1/x$ to get a quadratic in $t$. Check which values of $t$ give real $x$; use the fact that $|x + 1/x| \geq 2$ for real $x \neq 0$.
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Correct Answer: (2)